A non-separable Christensen's theorem and set tri-quotient maps

Simple item page
dc.creatorNedev, S.
dc.creatorPelant, J.
dc.creatorValov, V.
dc.date2008-01-11
dc.date2008-01-19
dc.date.accessioned2026-07-07T08:55:14Z
dc.date.available2026-07-07T08:55:14Z
dc.descriptionFor every space $X$ let $\mathcal K(X)$ be the set of all compact subsets of $X$. Christensen \cite{c:74} proved that if $X, Y$ are separable metrizable spaces and $F\colon\mathcal{K}(X)\to\mathcal{K}(Y)$ is a monotone map such that any $L\in\mathcal{K}(Y)$ is covered by $F(K)$ for some $K\in\mathcal{K}(X)$, then $Y$ is complete provided $X$ is complete. It is well known \cite{bgp} that this result is not true for non-separable spaces. In this paper we discuss some additional properties of $F$ which guarantee the validity of Christensen's result for more general spaces.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/0801.1717
dc.identifierhttp://arxiv.org/abs/0801.1717
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146207
dc.subjectGeneral Topology
dc.subject54C60 (Primary); 54E50 (Secondary)
dc.titleA non-separable Christensen's theorem and set tri-quotient maps
dc.typetext

Files

Collections

arXiv