Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6424738 | Topology and its Applications | 2012 | 8 Pages |
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 Îºâ©¾Î»â©¾Ï that (X,T), if κ-resolvable, admits an expansion UâT, 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
Authors
W.W. Comfort, Wanjun Hu,