Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9516957 | Topology and its Applications | 2005 | 11 Pages |
Abstract
Let X be a completely regular T1-space. A zero-set Z in X is called a full zero-set if clβXZ is a zero-set in the Äech-Stone compactification βX of X. As an generalization of theorems by W.G. McArthur and V. V. Uspenskii, we prove that every bounded, full zero-set F in X is compact if either (i) X has a regular Gδ-diagonal or (ii) X is a Baire space such that every open cover has a Ï-point-finite open refinement. In case (i), F is metrizable by Å neıËder's theorem. We also apply this to show that if the Dieudonné completion μX of X is a paracompact M-space, then X is metrizable if either (i) or (iii) X is a Baire space with a Ï-point-finite base.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Lei Mou,