Continuous and proper decompositions
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 by G. K. Williams PDF
 Proc. Amer. Math. Soc. 28 (1971), 267270 Request permission
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.References

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Additional Information
 © Copyright 1971 American Mathematical Society
 Journal: Proc. Amer. Math. Soc. 28 (1971), 267270
 MSC: Primary 54.60
 DOI: https://doi.org/10.1090/S00029939197102735834
 MathSciNet review: 0273583