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

 

Applications of cluster sets in minimal topological spaces


Author: T. R. Hamlett
Journal: Proc. Amer. Math. Soc. 53 (1975), 477-480
MSC: Primary 54D25; Secondary 54C10
MathSciNet review: 0388342
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Abstract: Given a function $ f$ from a topological space $ X$ into a topological space $ Y$ and a point $ x\epsilon X$, the cluster set of $ f$ at $ x$ is $ \mathcal{C}(f;x) = \cap \{ \operatorname{Cl} (f(U)):\;U\;{\text{is a neighborhood of }}x\} $, where $ \operatorname{Cl} (U)$ denotes the closure of $ U$. In this paper, $ Y$ is taken to be a minimal topological space and $ \mathcal{C}(f;x)$ is used as a tool to obtain information about the continuity of $ f$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0388342-5
PII: S 0002-9939(1975)0388342-5
Keywords: Almost continuous, cluster set, $ H$-closed, minimal Hausdorff, minimal regular, open filterbase, regular closed
Article copyright: © Copyright 1975 American Mathematical Society