Article ID Journal Published Year Pages File Type
4657761 Topology and its Applications 2016 10 Pages PDF
Abstract

We study the internal structure of topological spaces X which can be represented as the union of a finite collection of subspaces belonging to some nice class of spaces. Several closely related structure theorems are established. In particular, they concern the finite unions of subspaces with the weight ≤τ, the finite unions of subspaces with a point-countable base, and the finite unions of metrizable subspaces. As a corollary, we extend to finite unions the classical Mischenko's Theorem on metrizability of compacta with a point-countable base [11] (see Theorem 11). A few other applications of the structure theorems are given, in particular, to homogeneous spaces ( Corollary 5 and Corollary 10).

Related Topics
Physical Sciences and Engineering Mathematics Geometry and Topology
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