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- W1983609793 abstract "In this paper we shall extend certain results on topological groups to uniform spaces. In Section 2 we generalize a result of Gleason [2]. In Section 3 we show that every uniformly locally compact space can be “approximated” by locally compact metrizable spaces. We then use the results of Section 2 to present a partial converse of this “approximation” result. We now fix our notation. If A is a subset of a set E and R is a subset of E x E, then we let R(A) = {y E E : (a, y) E R for some a E A}. An equivalence relation R on a topological space E is said to be open (respectively, compact) if R(A) is open (respectively, compact) for each open (respectively, compact) subset A of E. We let E[@] d enote a uniform space with uniform structure %. Following Weil[6], we say that a uniform space E[G!Y] is uniformly locally compact if % is a separated, uniform structure on E and there is an entourage U in 4, such that for each x E E, U(x) is compact. If E is a locally compact metrizable space, then ([l], IX 9.4) there is a metric d on E, compatible with the topology of E, such that (E, d) is uniformly locally compact. I would like to thank Professor Ky Fan for his many valuable suggestions." @default.
- W1983609793 created "2016-06-24" @default.
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- W1983609793 date "1970-05-01" @default.
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- W1983609793 title "On uniformly locally compact spaces" @default.
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- W1983609793 doi "https://doi.org/10.1016/0022-247x(70)90173-3" @default.
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