| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4661368 | Topology and its Applications | 2007 | 7 Pages |
Abstract
We show that the cardinality of any space X with Δ-power homogeneous semiregularization that is either Urysohn or quasiregular is bounded by 2c(X)πχ(X). This improves a result of G.J. Ridderbos who showed this bound holds for Δ-power homogeneous regular spaces. By introducing the notion of a local πθ-base, we show that this bound can be further sharpened. We also show that no H-closed extremally disconnected space is power homogeneous. This is a variation of a result of K. Kunen who showed that no compact F-space is power homogeneous.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
