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Proceedings of the American Mathematical Society

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



Continuous and proper decompositions

Author: G. K. Williams
Journal: Proc. Amer. Math. Soc. 28 (1971), 267-270
MSC: Primary 54.60
MathSciNet review: 0273583
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Abstract: If $X$ is a locally connected, locally peripherally compact Hausdorff space and if $R$ is an equivalence relation on $X$ with fibers which are connected with compact boundaries, then it is shown that three definitions of continuity of $R$ are equivalent. Some of the propositions used to obtain this result are then applied to get sufficient conditions for a decomposition of certain types of metric spaces to be proper.

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Keywords: Semicontinuous decompositions, continuous decompositions, proper decompositions, open equivalence relation, closed equivalence relation, semiclosed equivalence relation, locally peripherally compact space
Article copyright: © Copyright 1971 American Mathematical Society