Hyperspaces of finite subsets, homeomorphic to pre-Hilbert spaces

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• 作者：Katsuhisa Koshino ^{pt120401we@kanagawa-u.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：54B20 ; 54F65 ; 57N20
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：1 September 2016
• 年：2016
• 卷：210
• 期：Complete
• 页码：133-143
• 全文大小：341 K

文摘

Let class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166864116301638&_mathId=si1.gif&_user=111111111&_pii=S0166864116301638&_rdoc=1&_issn=01668641&md5=3a1e090f4ce1f34ed7b5e0f37f82429a" title="Click to view the MathML source">Fin(X)class="mathContainer hidden">class="mathCode">$\mathrm{Fin}(X)$ be the hyperspace consisting of non-empty finite subsets of a topological space X endowed with the Vietoris topology. In this paper, we characterize topological spaces X   whose hyperspace class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166864116301638&_mathId=si1.gif&_user=111111111&_pii=S0166864116301638&_rdoc=1&_issn=01668641&md5=3a1e090f4ce1f34ed7b5e0f37f82429a" title="Click to view the MathML source">Fin(X)class="mathContainer hidden">class="mathCode">$\mathrm{Fin}(X)$ is homeomorphic to the pre-Hilbert space class="mathmlsrc">class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166864116301638&_mathId=si2.gif&_user=111111111&_pii=S0166864116301638&_rdoc=1&_issn=01668641&md5=4089725f5e10960a863dc1b1f084ef12">class="imgLazyJSB inlineImage" height="20" width="38" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0166864116301638-si2.gif">class="mathContainer hidden">class="mathCode">${\ell }_2^f(\kappa )$ for an uncountable cardinal κ.