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Locally Compact Path Spaces

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Abstract

It is shown that the space X [0,1], of continuous maps [0,1]→X with the compact-open topology, is not locally compact for any space X having a nonconstant path of closed points. For a T 1-space X, it follows that X [0,1] is locally compact if and only if X is locally compact and totally path-disconnected.

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Authors and Affiliations

  1. Union College, Schenectady, NY, 12308, U.S.A.

    S. B. Niefield

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  1. S. B. Niefield
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Correspondence to S. B. Niefield.

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Mathematics Subject Classifications (2000)

54C35, 54E45, 55P35, 18B30, 18D15.

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Niefield, S.B. Locally Compact Path Spaces. Appl Categor Struct 13, 65–69 (2005). https://doi.org/10.1007/s10485-004-5012-0

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  • DOI: https://doi.org/10.1007/s10485-004-5012-0

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