Non-Metrizable Uniformities and Proximities on Metrizable Spaces
In the literature there exist examples of metrizable spaces admitting nonmetrizable uniformities (e.g., see [3, Problem C, p. 204]). In this paper, this phenomenon is presented more coherently by showing that every non-compact metrizable space admits at least one non-metrizable proximity and uncountably many non-metrizable uniformities. It is also proved that the finest compatible uniformity (proximity) on a non-compact non-semidiscrete space is always non-metrizable.
1995 ◽
Vol 06
(04)
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pp. 625-643
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1970 ◽
Vol 22
(2)
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pp. 372-375
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Keyword(s):
2003 ◽
Vol 74
(88)
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pp. 121-128
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1978 ◽
Vol 30
(02)
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pp. 301-314
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1983 ◽
Vol 3
(2)
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pp. 167-185
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