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Proceedings of the American Mathematical Society

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

 

 

Continuum neighborhoods and filterbases


Authors: David P. Bellamy and Harvey S. Davis
Journal: Proc. Amer. Math. Soc. 27 (1971), 371-374
MSC: Primary 54.20
DOI: https://doi.org/10.1090/S0002-9939-1971-0276913-2
MathSciNet review: 0276913
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Abstract: In this paper we prove that if $ \Gamma $ is a filterbase of closed subsets of a compact Hausdorff space then $ T( \bigcap \Gamma ) = \bigcap \{ T(G)\vert G \in \Gamma \} $, where $ T(A)$ denotes the set of those points for which every neighborhood which is a continuum intersects $ A$ nonvoidly.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0276913-2
Keywords: Compact Hausdorff space, continuum neighborhood, $ T(A)$, $ T$-additive, filterbase, component
Article copyright: © Copyright 1971 American Mathematical Society