Preservation of complete metrizability by covering maps

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• 作者：Alexey Ostrovsky ^{Alexei.Ostrovski@gmx.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 54E40 ; 54C05 ; 54C10 ; secondary ; 26A15 ; 46A30 ; 97I30
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：15 March 2016
• 年：2016
• 卷：201
• 期：Complete
• 页码：269-273
• 全文大小：242 K

文摘

A map f:X→Y$f:X\to Y$ is said to be w-covering if for every ordinal α   and every compact S⊂Y$S\subset Y$ such that the α  -th Cantor derivative (S)^α${(S)}^{\alpha }$ of S   is a singleton {y}$\{y\}$ there is a compact subset E of X   such that f(E)⊂S$f(E)\subset S$ and a1521809483b54a8b0" title="Click to view the MathML source">(f(E))^α={y}${(f(E))}^{\alpha }=\{y\}$.

We investigate the preservation of completely metrizability by various kinds of w-covering maps.