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32

ACS
2005

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Locally Compact Path Spaces

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Locally Compact Path Spaces

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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 T1-space X, it follows that X[0,1] is locally compact if and only if X is locally compact and totally path-disconnected. AMS Classification: 54C35, 54E45, 55P35, 18B30, 18D15 Key Words: locally compact, compact-open topology, path space

Susan B. Niefield

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Added	15 Dec 2010
Updated	15 Dec 2010
Type	Journal
Year	2005
Where	ACS
Authors	Susan B. Niefield

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