Bicompleteness of the fine quasi-uniformity
1991 ◽
Vol 109
(1)
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pp. 167-186
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AbstractA characterization of the topological spaces that possess a bicomplete fine quasi-uniformity is obtained. In particular we show that the fine quasi-uniformity of each sober space, of each first-countable T1-space and of each quasi-pseudo-metrizable space is bicomplete. Moreover we give examples of T1-spaces that do not admit a bicomplete quasi-uniformity.We obtain several conditions under which the semi-continuous quasi-uniformity of a topological space is bicomplete and observe that the well-monotone covering quasiuniformity of a topological space is bicomplete if and only if the space is quasi-sober.
2001 ◽
Vol 27
(8)
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pp. 505-512
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1972 ◽
Vol 6
(1)
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pp. 107-115
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2016 ◽
Vol 5
(2)
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pp. 1-12
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2015 ◽
Vol 26
(03)
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pp. 1550032
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1968 ◽
Vol 20
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pp. 795-804
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Keyword(s):