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A Characterization of Spaces on Which all Path Maps are Continuous

P. W. Harley III
Proceedings of the American Mathematical Society
Vol. 34, No. 2 (Aug., 1972), pp. 621-622
DOI: 10.2307/2038418
Stable URL: http://www.jstor.org/stable/2038418
Page Count: 2
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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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