Article ID Journal Published Year Pages File Type
6424738 Topology and its Applications 2012 8 Pages PDF
Abstract

For a cardinal κ>1, a space X=(X,T) is κ-resolvable if X admits κ-many pairwise disjoint T-dense subsets; (X,T) is exactly κ-resolvable if it is κ-resolvable but not κ+-resolvable.The present paper complements and supplements the authorsʼ earlier work, which showed for suitably restricted spaces (X,T) and cardinals κ⩾λ⩾ω that (X,T), if κ-resolvable, admits an expansion U⊇T, with (X,U) Tychonoff if (X,T) is Tychonoff, such that (X,U) is μ-resolvable for all μ<λ but is not λ-resolvable (cf. Comfort and Hu, 2010 [11, Theorem 3.3]). Here the “finite case” is addressed. The authors show in ZFC for 1

Related Topics
Physical Sciences and Engineering Mathematics Geometry and Topology
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