Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54D25, 54C10

Retrieve articles in all journals with MSC: 54D25, 54C10

Additional Information

Keywords: Almost continuous, cluster set, $ H$-closed, minimal Hausdorff, minimal regular, open filterbase, regular closed
Article copyright: © Copyright 1975 American Mathematical Society