Functional characterizations of p-spaces
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AbstractWe show that a completely regular space Y is a p-space (a Čech-complete space, a locally compact space) if and only if given a dense subspace A of any topological space X and a continuous f: A → Y there are a p-embedded subset (resp. a G δ-subset, an open subset) M of X containing A and a quasicontinuous subcontinuous extension f*: M → Y of f continuous at every point of A. A result concerning a continuous extension to a residual set is also given.
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1968 ◽
Vol 8
(4)
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pp. 755-765
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1961 ◽
Vol 47
(7)
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pp. 1055-1057
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1973 ◽
Vol 25
(2)
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pp. 252-260
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1972 ◽
Vol 24
(1)
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pp. 29-37
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1974 ◽
Vol 26
(4)
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pp. 920-930
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2007 ◽
Vol 154
(14)
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pp. 2607-2634
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2013 ◽
Vol 176
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pp. 23-41
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2018 ◽
Vol 52
(3 (247))
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pp. 161-165
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