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Proceedings of the American Mathematical Society

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A characterization of local compactness

Author: R. V. Fuller
Journal: Proc. Amer. Math. Soc. 37 (1973), 615-616
MSC: Primary 54D45
MathSciNet review: 0317278
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Abstract: In this paper we show that the cluster set of a filter in a Hausdorff space X is a continuous function of the filter if and only if X is locally compact.

References [Enhancements On Off] (What's this?)

  • [1] J. L. Kelley, General topology, Van Nostrand, Princeton, N.J., 1955. MR 16, 1136. MR 0070144 (16:1136c)
  • [2] Oswald Wyler, A characterization of regularity in topology, Proc. Amer. Math. Soc. 29 (1971), 588-590. MR 43 #6865. MR 0281146 (43:6865)

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Keywords: Local compactness, space of filters, cluster set of a filter, lower semifinite topology
Article copyright: © Copyright 1973 American Mathematical Society

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