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)

 

 

A refinement on Michael's characterization of paracompactness


Author: H. H. Hung
Journal: Proc. Amer. Math. Soc. 83 (1981), 179-182
MSC: Primary 54D20
DOI: https://doi.org/10.1090/S0002-9939-1981-0620008-9
MathSciNet review: 620008
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that a $ {T_1}$ space is paracompact (and Hausdorff) if (and only if) every well (but arbitrarily) ordered open cover has an open refinement in the form of a countable union of families, (each of which being well ordered by the naturally induced well order) the initial segments of each of which are cushioned in the corresponding initial segments of the cover, i.e., the closures of the unions of the initial segments of each of which are contained within the unions of the corresponding initial segments of the cover.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54D20

Retrieve articles in all journals with MSC: 54D20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0620008-9
Keywords: Paracompactness, covers, well orders, cushioning requirements only on initial segments with respect to these well orders
Article copyright: © Copyright 1981 American Mathematical Society