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Proceedings of the American Mathematical Society

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



Multifunctions and cluster sets

Author: James E. Joseph
Journal: Proc. Amer. Math. Soc. 74 (1979), 329-337
MSC: Primary 54C60; Secondary 54D20
MathSciNet review: 524312
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Abstract: In this article the notion of cluster set-which has been extensively studied within the framework of real and analytic function theory and to some extent for arbitrary functions between arbitrary topological spaces-is investigated for multifunctions. We generalize the notion of cluster set, extend and generalize some results for cluster sets of functions, and offer some results for multifunctions which are new for functions. In the last section, several compactness generalizations are characterized in terms of multifunctions and cluster sets.

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Keywords: Multifunctions, cluster sets, $ \theta $-closed subsets, closed graph, quasi H-closed subset relative to a space
Article copyright: © Copyright 1979 American Mathematical Society

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