{"id":12246,"date":"2025-01-01T08:29:26","date_gmt":"2025-01-01T08:29:26","guid":{"rendered":"https:\/\/www.hnjournal.net\/?page_id=12246"},"modified":"2025-01-10T12:51:05","modified_gmt":"2025-01-10T12:51:05","slug":"6-1-18","status":"publish","type":"page","link":"https:\/\/www.hnjournal.net\/ar\/6-1-18\/","title":{"rendered":""},"content":{"rendered":"<div class=\"journal-article\" style=\"margin-bottom: 20px;\"><h3 style='text-align: left; font-family:Times New Roman;'>Analysis of Homeomorphism Groups for Finite Spaces with Small Cardinality Using Burnside&#039;s Theorem and the Semidirect Product<\/h3><h4 style='text-align: right; font-family:Simplified Arabic;'>\u062a\u062d\u0644\u064a\u0644 \u0632\u0645\u0631 \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u0627\u062a \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u064a\u0629 \u0644\u0644\u0645\u0633\u0627\u062d\u0627\u062a \u0627\u0644\u0637\u0648\u0628\u0648\u0644\u0648\u062c\u064a\u0629 \u0627\u0644\u0645\u0646\u062a\u0647\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062c\u0645 \u0627\u0644\u0635\u063a\u064a\u0631 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0628\u0631\u0647\u0646\u0629 \u0628\u064a\u0631\u0646\u0633\u0627\u064a\u062f \u0648\u0627\u0644\u0637\u0631\u064a\u0642\u0647  \u0634\u0628\u0647 \u0627\u0644\u0645\u0628\u0627\u0634\u0631<\/h4><p style='text-align: left; font-weight:bold;'>Enas M. Almeehob <sup>1<\/sup><\/p><div style='direction: ltr; text-align: left; font-size:12px; line-height:1.5;'><p>Department of Mathematics ,Faculty of Arts and Sciences \u2013Al-Marj ,Benghazi University ,Libya. Email: inaasmesmari@gmail.com<\/p><\/div><p style='text-align:left;'><strong>DOI:<\/strong> <a href='https:\/\/doi.org\/https:\/\/doi.org\/10.53796\/hnsj61\/18' target='_blank' rel='noopener'>https:\/\/doi.org\/10.53796\/hnsj61\/18<\/a><\/p><p style='text-align: left;'><strong>Arabic Scientific Research Identifier:<\/strong> <a href='https:\/\/arsri.org\/10000\/61\/18' target='_blank' rel='noopener'>https:\/\/arsri.org\/10000\/61\/18<\/a><\/p><p style='text-align: left;'><strong>Volume (6) Issue (1). Pages:<\/strong> 294 - 300<\/p><p style='text-align: left;'><strong>Received at:<\/strong> 2024-12-04 | <strong>Accepted at:<\/strong> 2024-12-15 | <strong>Published at:<\/strong> 2025-01-01<\/p><p><a href='\/volume6\/issue1\/6-1-18.pdf' target='_blank' rel='noopener' style='background-color:green;color:white;padding:10px 15px;text-decoration:none;border-radius:5px;'>Download PDF<\/a><\/p>\r\n<style>\r\n.hnsj-cite-btn{\r\n  display:inline-flex; gap:8px; align-items:center;\r\n  padding:10px 14px; border-radius:10px;\r\n  border:1px solid #0b5ed7; background:#0b5ed7; color:#fff;\r\n  cursor:pointer; font-weight:700;\r\n}\r\n.hnsj-cite-btn:hover{background:#084bb0;border-color:#084bb0}\r\n.hnsj-cite-note{display:block;margin-top:6px;font-size:13px;opacity:.85}\r\n\r\n.hnsj-modal-backdrop{\r\n  position:fixed; inset:0; background:rgba(0,0,0,.55);\r\n  display:none; z-index:99998;\r\n}\r\n.hnsj-modal{\r\n  position:fixed; left:50%; top:50%; transform:translate(-50%,-50%);\r\n  width:min(760px,94vw); background:#fff; border-radius:14px;\r\n  box-shadow:0 12px 35px rgba(0,0,0,.28);\r\n  display:none; z-index:99999; overflow:hidden;\r\n  border:1px solid rgba(0,0,0,.08);\r\n}\r\n\r\n.hnsj-modal-header{\r\n  display:flex; justify-content:space-between; align-items:center;\r\n  padding:14px 16px; border-bottom:1px solid #eee; background:#f8fafc;\r\n}\r\n.hnsj-modal-title{font-size:16px;font-weight:800;color:#111827}\r\n.hnsj-modal-close{\r\n  border:1px solid #d1d5db; background:#fff;\r\n  width:34px; height:34px; border-radius:10px;\r\n  font-size:18px; cursor:pointer; line-height:0; color:#111827;\r\n}\r\n.hnsj-modal-close:hover{background:#f3f4f6}\r\n\r\n.hnsj-tabs{\r\n  display:flex; gap:10px; padding:10px 16px;\r\n  border-bottom:1px solid #f0f0f0; justify-content:flex-end;\r\n}\r\n.hnsj-tab{\r\n  padding:10px 14px; border-radius:10px;\r\n  border:1px solid #cfcfcf; background:#f3f4f6;\r\n  cursor:pointer; font-weight:800; color:#111827;\r\n}\r\n.hnsj-tab:hover{background:#e5e7eb;border-color:#9ca3af}\r\n.hnsj-tab.active{\r\n  background:#0b5ed7; border-color:#0b5ed7; color:#fff;\r\n  box-shadow:0 2px 10px rgba(11,94,215,.18);\r\n}\r\n\r\n.hnsj-modal-body{padding:14px 16px}\r\n.hnsj-row{\r\n  display:flex; gap:10px; flex-wrap:wrap; align-items:center;\r\n  margin-bottom:10px; justify-content:flex-end;\r\n}\r\n.hnsj-select{\r\n  padding:10px 12px; border-radius:10px;\r\n  border:1px solid #cfcfcf; min-width:220px;\r\n  background:#fff; color:#111827; font-weight:700;\r\n}\r\n.hnsj-copy{\r\n  padding:10px 14px; border-radius:10px;\r\n  border:1px solid #0b5ed7; background:#0b5ed7; color:#fff;\r\n  cursor:pointer; font-weight:800;\r\n}\r\n.hnsj-copy:hover{background:#084bb0;border-color:#084bb0}\r\n\r\n.hnsj-textarea{\r\n  width:100%; min-height:130px; padding:12px;\r\n  border-radius:12px; border:1px solid #cfcfcf;\r\n  line-height:1.7; resize:vertical; color:#111827; background:#fff;\r\n}\r\n.hnsj-actions{display:flex; justify-content:space-between; align-items:center; margin-top:10px; gap:10px; flex-wrap:wrap;}\r\n.hnsj-dl{\r\n  padding:10px 14px;\r\n  border-radius:10px;\r\n  border:1px solid #0b5ed7;\r\n  background:#0b5ed7;\r\n  color:#fff;\r\n  cursor:pointer;\r\n  font-weight:800;\r\n}\r\n.hnsj-dl:hover{background:#084bb0;border-color:#084bb0}\r\n\/* Force the citation modal UI to be independent from site RTL\/LTR *\/\r\n.hnsj-modal,\r\n.hnsj-modal *{\r\n  direction: ltr;\r\n  text-align: left;\r\n}\r\n\r\n\/* Keep the header title readable *\/\r\n.hnsj-modal-header{\r\n  direction: ltr;\r\n}\r\n<\/style>\r\n\r\n<script>\r\n(function(){\r\n  function slugifyFileName(s){\r\n    return (s || 'citation')\r\n      .toString()\r\n      .trim()\r\n      .replace(\/^https?:\\\/\\\/\/i,'')\r\n      .replace(\/[^a-z0-9]+\/gi,'-')\r\n      .replace(\/-+\/g,'-')\r\n      .replace(\/^-|-$\/g,'')\r\n      .toLowerCase();\r\n  }\r\n\r\n  function downloadTextFile(filename, content, mime){\r\n    var blob = new Blob([content], { type: mime || 'text\/plain;charset=utf-8' });\r\n    var url = URL.createObjectURL(blob);\r\n    var a = document.createElement('a');\r\n    a.href = url;\r\n    a.download = filename;\r\n    document.body.appendChild(a);\r\n    a.click();\r\n    a.remove();\r\n    setTimeout(function(){ URL.revokeObjectURL(url); }, 500);\r\n  }\r\n\r\n  function splitAuthors(str){\r\n    if(!str) return [];\r\n    return str\r\n      .split(\/,|\u061b|\u060c|;|\\n\/g)\r\n      .map(s => s.trim())\r\n      .filter(Boolean);\r\n  }\r\n\r\n  function buildRIS(m, langKey){\r\n    const title   = (langKey === 'ar') ? 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M. (2025). Analysis of Homeomorphism Groups for Finite Spaces with Small Cardinality Using Burnside&#039;s Theorem and the Semidirect Product. Humanities &amp; Natural Sciences Journal, 6(1). https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj61\\\/18&quot;,&quot;Chicago&quot;:&quot;Eenas M. Almeehoub. 2025. \\&quot;Analysis of Homeomorphism Groups for Finite Spaces with Small Cardinality Using Burnside&#039;s Theorem and the Semidirect Product.\\&quot; Humanities &amp; Natural Sciences Journal 6, no. 1. https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj61\\\/18&quot;,&quot;Harvard&quot;:&quot;Almeehoub E. M. 2025. Analysis of Homeomorphism Groups for Finite Spaces with Small Cardinality Using Burnside&#039;s Theorem and the Semidirect Product. Humanities &amp; Natural Sciences Journal. [Internet] 2025-01-01. [Cited 2026-04-24]. 6(1). Available at: https:\\\/\\\/www.hnjournal.net\\\/6-1-18\\\/. https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj61\\\/18&quot;,&quot;Vancouver&quot;:&quot;Almeehoub E. M. Analysis of Homeomorphism Groups for Finite Spaces with Small Cardinality Using Burnside&#039;s Theorem and the Semidirect Product. Humanities &amp; Natural Sciences Journal. [Internet]. 2025-01-01; 6(1). Available from: https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj61\\\/18&quot;,&quot;IEEE&quot;:&quot;Almeehoub E. M, \\&quot;Analysis of Homeomorphism Groups for Finite Spaces with Small Cardinality Using Burnside&#039;s Theorem and the Semidirect Product,\\&quot; Humanities &amp; Natural Sciences Journal, vol. 6, no. 1, 2025. https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj61\\\/18&quot;,&quot;MLA&quot;:&quot;Eenas M. Almeehoub. \\&quot;Analysis of Homeomorphism Groups for Finite Spaces with Small Cardinality Using Burnside&#039;s Theorem and the Semidirect Product.\\&quot; Humanities &amp; Natural Sciences Journal, vol. 6, no. 1, 2025-01-01, https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj61\\\/18&quot;}' data-cit-ar='{&quot;APA&quot;:&quot;Almeehob E M.. (2025). \u062a\u062d\u0644\u064a\u0644 \u0632\u0645\u0631 \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u0627\u062a \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u064a\u0629 \u0644\u0644\u0645\u0633\u0627\u062d\u0627\u062a \u0627\u0644\u0637\u0648\u0628\u0648\u0644\u0648\u062c\u064a\u0629 \u0627\u0644\u0645\u0646\u062a\u0647\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062c\u0645 \u0627\u0644\u0635\u063a\u064a\u0631 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0628\u0631\u0647\u0646\u0629 \u0628\u064a\u0631\u0646\u0633\u0627\u064a\u062f \u0648\u0627\u0644\u0637\u0631\u064a\u0642\u0647  \u0634\u0628\u0647 \u0627\u0644\u0645\u0628\u0627\u0634\u0631. \u0645\u062c\u0644\u0629 \u0627\u0644\u0639\u0644\u0648\u0645 \u0627\u0644\u0627\u0646\u0633\u0627\u0646\u064a\u0629 \u0648\u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629\u060c 6(1). https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj61\\\/18&quot;,&quot;Chicago&quot;:&quot;Enas M. Almeehob. 2025. \u00ab\u062a\u062d\u0644\u064a\u0644 \u0632\u0645\u0631 \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u0627\u062a \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u064a\u0629 \u0644\u0644\u0645\u0633\u0627\u062d\u0627\u062a \u0627\u0644\u0637\u0648\u0628\u0648\u0644\u0648\u062c\u064a\u0629 \u0627\u0644\u0645\u0646\u062a\u0647\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062c\u0645 \u0627\u0644\u0635\u063a\u064a\u0631 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0628\u0631\u0647\u0646\u0629 \u0628\u064a\u0631\u0646\u0633\u0627\u064a\u062f \u0648\u0627\u0644\u0637\u0631\u064a\u0642\u0647  \u0634\u0628\u0647 \u0627\u0644\u0645\u0628\u0627\u0634\u0631\u00bb. \u0645\u062c\u0644\u0629 \u0627\u0644\u0639\u0644\u0648\u0645 \u0627\u0644\u0627\u0646\u0633\u0627\u0646\u064a\u0629 \u0648\u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629\u060c 6(1). https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj61\\\/18&quot;,&quot;Harvard&quot;:&quot;Almeehob E M.. \u062a\u062d\u0644\u064a\u0644 \u0632\u0645\u0631 \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u0627\u062a \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u064a\u0629 \u0644\u0644\u0645\u0633\u0627\u062d\u0627\u062a \u0627\u0644\u0637\u0648\u0628\u0648\u0644\u0648\u062c\u064a\u0629 \u0627\u0644\u0645\u0646\u062a\u0647\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062c\u0645 \u0627\u0644\u0635\u063a\u064a\u0631 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0628\u0631\u0647\u0646\u0629 \u0628\u064a\u0631\u0646\u0633\u0627\u064a\u062f \u0648\u0627\u0644\u0637\u0631\u064a\u0642\u0647  \u0634\u0628\u0647 \u0627\u0644\u0645\u0628\u0627\u0634\u0631. \u0645\u062c\u0644\u0629 \u0627\u0644\u0639\u0644\u0648\u0645 \u0627\u0644\u0627\u0646\u0633\u0627\u0646\u064a\u0629 \u0648\u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629. [\u0627\u0646\u062a\u0631\u0646\u062a] 2025-01-01. [\u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0648\u0635\u0648\u0644 2026-04-24]. 6(1). \u0645\u062a\u0627\u062d \u0639\u0644\u0649: https:\\\/\\\/www.hnjournal.net\\\/6-1-18\\\/. https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj61\\\/18&quot;,&quot;Vancouver&quot;:&quot;Almeehob E M.. \u062a\u062d\u0644\u064a\u0644 \u0632\u0645\u0631 \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u0627\u062a \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u064a\u0629 \u0644\u0644\u0645\u0633\u0627\u062d\u0627\u062a \u0627\u0644\u0637\u0648\u0628\u0648\u0644\u0648\u062c\u064a\u0629 \u0627\u0644\u0645\u0646\u062a\u0647\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062c\u0645 \u0627\u0644\u0635\u063a\u064a\u0631 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0628\u0631\u0647\u0646\u0629 \u0628\u064a\u0631\u0646\u0633\u0627\u064a\u062f \u0648\u0627\u0644\u0637\u0631\u064a\u0642\u0647  \u0634\u0628\u0647 \u0627\u0644\u0645\u0628\u0627\u0634\u0631. \u0645\u062c\u0644\u0629 \u0627\u0644\u0639\u0644\u0648\u0645 \u0627\u0644\u0627\u0646\u0633\u0627\u0646\u064a\u0629 \u0648\u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629. [\u0627\u0646\u062a\u0631\u0646\u062a]. 2025-01-01\u061b 6(1). \u0645\u062a\u0627\u062d \u0645\u0646: https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj61\\\/18&quot;,&quot;IEEE&quot;:&quot;Almeehob E M.. \u00ab\u062a\u062d\u0644\u064a\u0644 \u0632\u0645\u0631 \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u0627\u062a \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u064a\u0629 \u0644\u0644\u0645\u0633\u0627\u062d\u0627\u062a \u0627\u0644\u0637\u0648\u0628\u0648\u0644\u0648\u062c\u064a\u0629 \u0627\u0644\u0645\u0646\u062a\u0647\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062c\u0645 \u0627\u0644\u0635\u063a\u064a\u0631 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0628\u0631\u0647\u0646\u0629 \u0628\u064a\u0631\u0646\u0633\u0627\u064a\u062f \u0648\u0627\u0644\u0637\u0631\u064a\u0642\u0647  \u0634\u0628\u0647 \u0627\u0644\u0645\u0628\u0627\u0634\u0631\u00bb. \u0645\u062c\u0644\u0629 \u0627\u0644\u0639\u0644\u0648\u0645 \u0627\u0644\u0627\u0646\u0633\u0627\u0646\u064a\u0629 \u0648\u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629\u060c \u0645 6\u060c \u0639 1\u060c 2025. https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj61\\\/18&quot;,&quot;MLA&quot;:&quot;Enas M. Almeehob. \u00ab\u062a\u062d\u0644\u064a\u0644 \u0632\u0645\u0631 \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u0627\u062a \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u064a\u0629 \u0644\u0644\u0645\u0633\u0627\u062d\u0627\u062a \u0627\u0644\u0637\u0648\u0628\u0648\u0644\u0648\u062c\u064a\u0629 \u0627\u0644\u0645\u0646\u062a\u0647\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062c\u0645 \u0627\u0644\u0635\u063a\u064a\u0631 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0628\u0631\u0647\u0646\u0629 \u0628\u064a\u0631\u0646\u0633\u0627\u064a\u062f \u0648\u0627\u0644\u0637\u0631\u064a\u0642\u0647  \u0634\u0628\u0647 \u0627\u0644\u0645\u0628\u0627\u0634\u0631\u00bb. \u0645\u062c\u0644\u0629 \u0627\u0644\u0639\u0644\u0648\u0645 \u0627\u0644\u0627\u0646\u0633\u0627\u0646\u064a\u0629 \u0648\u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629\u060c \u0645 6\u060c \u0639 1\u060c 2025-01-01\u060c https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj61\\\/18&quot;}'>\r\n    <div class='hnsj-modal-header'>\r\n    <div class='hnsj-modal-title'>Cite \/ \u0627\u0644\u0627\u0633\u062a\u0634\u0647\u0627\u062f<\/div>\r\n    <button class='hnsj-modal-close' type='button' data-hnsj-close aria-label='Close'>\u00d7<\/button>\r\n    <\/div>\r\n\r\n    <div class='hnsj-tabs'>\r\n      <button type='button' class='hnsj-tab active' data-lang='en'>English (Roman)<\/button>\r\n      <button type='button' class='hnsj-tab' data-lang='ar'>\u0627\u0644\u0639\u0631\u0628\u064a\u0629<\/button>\r\n    <\/div>\r\n\r\n    <div class='hnsj-modal-body'>\r\n      <div class='hnsj-row'>\r\n        <button type='button' class='hnsj-copy' data-hnsj-copy>Copy<\/button>\r\n        <select class='hnsj-select' data-hnsj-style><\/select>\r\n        <\/div>\r\n\r\n      <textarea class='hnsj-textarea' data-hnsj-box readonly><\/textarea>\r\n\r\n      <div class='hnsj-actions'>\r\n        <div style='display:flex; gap:10px; flex-wrap:wrap;'>\r\n          <button type='button' class='hnsj-dl' data-hnsj-dl='ris'>Download RIS<\/button>\r\n          <button type='button' class='hnsj-dl' data-hnsj-dl='bib'>Download BibTeX<\/button>\r\n        <\/div>\r\n      <\/div>\r\n    <\/div>\r\n  <\/div>\r\n<\/div>\r\n<p style='text-align:justify; direction:ltr;'><strong>Abstract:<\/strong> In this article, I compute the number of orbit spaces for finite spaces \u2223X\u2223\u22644 using Burnside's Counting Theorem. The group Homeo(X), consisting of all homeomorphisms from a space X onto itself for \u2223X\u2223\u22644 ,is calculated using two different methods that yield identical results. These findings contribute to the understanding of the algebraic structure of finite spaces and their applications in mathematics (Elmsmary, 2016).<\/p><p style='text-align:left; direction:ltr;'><strong>Keywords: <\/strong> homeomorphism group, split exact sequence ,semi direct product, Burnside&#039;s counting theorem, finite topological spaces.<\/p><p style='text-align:justify; direction:rtl;'><strong>\u0627\u0644\u0645\u0633\u062a\u062e\u0644\u0635: <\/strong> \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0628\u062d\u062b\u060c \u0646\u0642\u0648\u0645 \u0628\u062d\u0633\u0627\u0628 \u0639\u062f\u062f \u0641\u0636\u0627\u0621\u0627\u062a \u0627\u0644\u0645\u062f\u0627\u0631\u0627\u062a \u0644\u0644\u0645\u0633\u0627\u062d\u0627\u062a \u0627\u0644\u0637\u0648\u0628\u0648\u0644\u0648\u062c\u064a\u0629 \u0627\u0644\u0645\u0646\u062a\u0647\u064a\u0629 \u2223X\u2223 \u2264 4 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0628\u0631\u0647\u0646\u0629 \u0628\u064a\u0631\u0646\u0633\u0627\u064a\u062f \u0644\u0644\u0639\u062f. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0646\u062d\u0633\u0628 \u0632\u0645\u0631\u0629 \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u0627\u062a \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u064a\u0629 Homeo(X)\u060c \u0627\u0644\u062a\u064a \u062a\u0645\u062b\u0644 \u062c\u0645\u064a\u0639 \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u0627\u062a \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u064a\u0629 \u0644\u0644\u0645\u0633\u0627\u062d\u0629 \u0639\u0644\u0649 \u0646\u0641\u0633\u0647\u0627\u060c \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u062d\u062c\u0645\u0647\u0627 \u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0637\u0631\u064a\u0642\u062a\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u062a\u064a\u0646 \u0641\u064a \u0627\u0644\u062d\u0633\u0627\u0628\u060c \u0648\u0643\u0644\u062a\u0627\u0647\u0645\u0627 \u0623\u0639\u0637\u062a \u0646\u0641\u0633 \u0627\u0644\u0646\u062a\u0627\u0626\u062c. \u0647\u0630\u0647 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u062a\u0633\u0627\u0647\u0645 \u0641\u064a \u062a\u0639\u0632\u064a\u0632 \u0627\u0644\u0641\u0647\u0645 \u062d\u0648\u0644 \u0627\u0644\u0628\u0646\u064a\u0629 \u0627\u0644\u062c\u0628\u0631\u064a\u0629 \u0644\u0644\u0645\u0633\u0627\u062d\u0627\u062a \u0627\u0644\u0645\u062a\u0646\u0627\u0647\u064a\u0629\u060c \u0648\u062a\u0648\u0636\u064a\u062d \u062a\u0637\u0628\u064a\u0642\u0627\u062a\u0647\u0627 \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a<\/p><\/div>\n\n\n<p dir=\"ltr\" style=\"text-align: justify;\"><strong>References: <\/strong><\/p>\n<ol dir=\"ltr\" style=\"text-align: justify;\">\n<li>Armstrong, M. A. (1988). <em>Groups and symmetry<\/em>. Springer.<\/li>\n<li>Dummit, D. S., &amp; Foote, R. M. (1999). <em>Abstract algebra<\/em>. Prentice Hall.<\/li>\n<li>Elmsmary, E. M. (2016). <em>Homomorphism groups of finite topological spaces<\/em> (Master&#8217;s thesis). Department of Mathematics, University of Benghazi.<\/li>\n<li>Hatcher, A. (2002). <em>Algebraic topology<\/em>. Cambridge University Press.<\/li>\n<li>Kelley, J. L. (2008). <em>General topology<\/em>. Ishi Press.<\/li>\n<li>Kono, S., &amp; Ushitaki, F. (2003). <em>Homeomorphism groups of finite topological spaces and group action<\/em>. Kyoto University.<\/li>\n<li>Kosnowski, C. (1980). <em>A first course in algebraic topology<\/em>. Cambridge University Press.<\/li>\n<li>Lee, J. M. (2011). <em>Introduction to topological manifolds<\/em> (2nd ed.). Springer.<\/li>\n<li>May, J. P. (1999). <em>A concise course in algebraic topology<\/em>. University of Chicago Press.<\/li>\n<\/ol>\n<p dir=\"ltr\" style=\"text-align: justify;\">Munkres, J. R. (2000). <em>Topology<\/em> (2nd ed.). Prentice Hall.<\/p>\n<ol dir=\"ltr\" style=\"text-align: justify;\">\n<li>Rotman, J. J. (2015). <em>An introduction to the theory of groups<\/em> (4th ed.). Springer.<\/li>\n<\/ol>\n<p dir=\"ltr\" style=\"text-align: justify;\">\u00a0<\/p>","protected":false},"excerpt":{"rendered":"<p>References: Armstrong, M. A. (1988). Groups and symmetry. Springer. Dummit, D. S., &amp; Foote, R. M. (1999). Abstract algebra. Prentice Hall. Elmsmary, E. M. (2016). Homomorphism groups of finite topological [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_joinchat":[],"footnotes":""},"class_list":["post-12246","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.hnjournal.net\/ar\/wp-json\/wp\/v2\/pages\/12246","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.hnjournal.net\/ar\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.hnjournal.net\/ar\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.hnjournal.net\/ar\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.hnjournal.net\/ar\/wp-json\/wp\/v2\/comments?post=12246"}],"version-history":[{"count":3,"href":"https:\/\/www.hnjournal.net\/ar\/wp-json\/wp\/v2\/pages\/12246\/revisions"}],"predecessor-version":[{"id":12475,"href":"https:\/\/www.hnjournal.net\/ar\/wp-json\/wp\/v2\/pages\/12246\/revisions\/12475"}],"wp:attachment":[{"href":"https:\/\/www.hnjournal.net\/ar\/wp-json\/wp\/v2\/media?parent=12246"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}