Some characterizations of COTS with endpoints

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• 作者：Devender Kumar Kamboj^a ; ^{kamboj.dev81@rediffmail.com" class="auth_mail" title="E-mail the corresponding author} ; Vinod Kumar^b ; ^{vkvinod96@yahoo.co.in" class="auth_mail" title="E-mail the corresponding author} ; Satbir Singh^c ; ^{satbir78r@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 54F05 ; 54F15
• 刊名：Topology and its Applications
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：194
• 期：Complete
• 页码：144-149
• 全文大小：274 K

文摘

We prove that a connected space X is a COTS with endpoints iff there is a one–one Darboux function from X onto a space with endpoints. Using this result, we show that a connected space X   is homeomorphic to the closed unit interval if it is class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S016686411500334X&_mathId=si1.gif&_user=111111111&_pii=S016686411500334X&_rdoc=1&_issn=01668641&md5=b31883f4c42faef4368f410641b4ba32" title="Click to view the MathML source">T₁class="mathContainer hidden">class="mathCode">$T_1$ separable and locally connected and there is a one–one Darboux function from X onto a space with endpoints. Also we obtain some other characterizations of COTS with endpoints and some characterizations of the closed unit interval.