Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Applications of shrinkable covers

Author: J. C. Smith
Journal: Proc. Amer. Math. Soc. 73 (1979), 379-387
MSC: Primary 54D15
MathSciNet review: 518525
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An open cover $ \mathcal{G} = \{ {G_\alpha }:\alpha \in A\} $ of a topological space X is shrinkable if there exists a closed cover $ \mathcal{F} = \{ {F_\alpha }:\alpha \in A\} $ of X such that $ {F_\alpha } \subseteq {G_\alpha }$ for each $ \alpha \in A$.

In this paper the author determines conditions necessary for a variety of general covers to be shrinkable. In particular it is shown that the shrinkability of special types of covers provide characterizations for normal and countably paracompact, normal spaces. The types of covers investigated are, weak $ \bar \theta $-covers, weak $ \bar \theta $-covers, point countable covers, $ \delta \theta $-covers and weak $ \overline {\delta \theta } $-covers. Applications of these results are answers of unsolved problems and new results for irreducible spaces.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54D15

Retrieve articles in all journals with MSC: 54D15

Additional Information

Keywords: Shrinkable, normal, countably paracompact, $ \theta $-refinable, weakly $ \theta $-refinable, weakly $ \theta $-refinable, point countable cover, $ \delta \theta $-refinable, weak $ \overline {\delta \theta } $-cover, irreducible, closure-preserving, sequential, countable tightness
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society