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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Inner points and breadth in certain compact semilattices


Authors: D. R. Brown and J. W. Stepp
Journal: Proc. Amer. Math. Soc. 84 (1982), 581-587
MSC: Primary 22A26; Secondary 22A15, 54H12
MathSciNet review: 643754
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Abstract: A point $ x \in X$ is inner if there exists an open set $ U$ containing $ x$ such that for each open set $ V$ with $ x \in V \subseteq U$, the inclusion homomorphism $ {i^* }:$: $ {H^*}(X,X \setminus V) \to {H^*}(X,X \setminus U)$ is nontrivial. In this note it is proved that, if $ X$ is a compact, chainwise connected topological semilattice of codimension $ n$, and $ x$ is a point of breadth $ n + 1$, then $ x$ is an inner point.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0643754-0
PII: S 0002-9939(1982)0643754-0
Keywords: Inner points, codimension
Article copyright: © Copyright 1982 American Mathematical Society