Applications of cluster sets in minimal topological spaces
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- by T. R. Hamlett PDF
- Proc. Amer. Math. Soc. 53 (1975), 477-480 Request permission
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 $f$.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 477-480
- MSC: Primary 54D25; Secondary 54C10
- DOI: https://doi.org/10.1090/S0002-9939-1975-0388342-5
- MathSciNet review: 0388342