×

zbMATH — the first resource for mathematics

Addition theorems for dense subspaces. (English) Zbl 1349.54062
Properties of Tychonoff spaces which can be represented as the union of finitely many dense metrizable (and related) subspaces are investigated. Many such spaces have nice properties. It is shown, for example, that a Lindelöf or pseudocompact space which is the union of finitely many dense metrizable subspaces is a separable metrizable space. A normal space \(X\) which is the union of a finite family of dense completely metrizable subspaces is also completely metrizable. If a space \(X\) is the union of finitely many dense Čech-complete Moore subspaces, then \(X\) is also a Čech-complete Moore space. A similar result states that if a space \(X\) is the union a locally finite family of Čech-complete Moore subspaces, then \(X\) contains an open dense Čech-complete Moore subspace.
MSC:
54E35 Metric spaces, metrizability
54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
54B05 Subspaces in general topology
PDF BibTeX XML Cite
Full Text: DOI