Proceedings of the American Mathematical Society

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

 

 

An example relating to Arhangelskiĭ's class $ {\rm MOBI}$


Author: James R. Boone
Journal: Proc. Amer. Math. Soc. 41 (1973), 615-618
MSC: Primary 54G20; Secondary 54D20
MathSciNet review: 0328891
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Abstract: A space in Arhangel'skiĭ's class MOBI is presented which fails to have two structural properties which are weaker than countable metacompactness. A space is countably metacompact if and only if it is countably $ \theta $-refinable and pointwise collectionwise normal for countable collections. This space does not have either of these properties.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0328891-7
Keywords: Arhangel'skiĭ's class MOBI, $ \theta $-refinable, pointwise collectionwise normal, countably metacompact
Article copyright: © Copyright 1973 American Mathematical Society