Separability of path spaces under the open-point and bi-point-open topologies
Keyword(s):
In [3], two new kinds of topologies called the open-point topology and the bi-point-open topology on C(X), the set of all real-valued continuous functions on a Tychonoff space X, have been introduced. In this article, we study the separability of the space P(X), of all continuous maps on [0; 1] into a Hausdorff space X, with the open-point and bi-point-open topologies. Our result also demonstrates, the claim made in [3], that both the domain as well as the codomain play significant roles in the construction of the open-point and bi-point-open topologies.
1981 ◽
Vol 33
(4)
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pp. 872-884
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1969 ◽
Vol 12
(3)
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pp. 327-331
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1971 ◽
Vol 23
(3)
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pp. 468-480
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1979 ◽
Vol 31
(4)
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pp. 890-896
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1975 ◽
Vol 19
(3)
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pp. 291-300
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1987 ◽
Vol 36
(2)
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pp. 267-278