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Proceedings of the American Mathematical Society

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

 

 

A characterization of spaces on which all path maps are continuous


Author: P. W. Harley
Journal: Proc. Amer. Math. Soc. 34 (1972), 621-622
MSC: Primary 54C10
DOI: https://doi.org/10.1090/S0002-9939-1972-0309050-X
MathSciNet review: 0309050
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Abstract: Here it is shown that all path maps on a topological space X are continuous if and only if X is a quotient image of a locally path connected metric space. This characterization strengthens results of E. Bedford [1].


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DOI: https://doi.org/10.1090/S0002-9939-1972-0309050-X
Keywords: Locally path connected, path maps, metric space, quotient maps
Article copyright: © Copyright 1972 American Mathematical Society