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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Condition for a function space to be locally compact


Author: R. V. Fuller
Journal: Proc. Amer. Math. Soc. 36 (1972), 615-617
MSC: Primary 54C35; Secondary 54B20
MathSciNet review: 0375217
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Abstract: Let F be an equicontinuous family of functions from a compact Hausdorff space to a locally compact Hausdorff uniform space. In this paper we prove that the pointwise closure of F is locally compact relative to the topology of uniform convergence.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0375217-8
PII: S 0002-9939(1972)0375217-8
Keywords: Function space, hyperspace, finite topology, upper semifinite topology, lower semifinite topology, topology of pointwise convergence, topology of uniform convergence, equicontinuous family of functions, graph of a function, graph topology
Article copyright: © Copyright 1972 American Mathematical Society