Conţinutul numărului revistei |
Articolul precedent |
Articolul urmator |
372 0 |
SM ISO690:2012 CHOBAN, Mitrofan, KENDEROV, Petar, REVALSKI, Julian Petrov. Spaces with fragmentable open sets. In: Topology and its Applications, 2020, nr. 281, p. 0. ISSN 0166-8641. DOI: https://doi.org/10.1016/j.topol.2020.107214 |
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Topology and its Applications | ||||||
Numărul 281 / 2020 / ISSN 0166-8641 | ||||||
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DOI:https://doi.org/10.1016/j.topol.2020.107214 | ||||||
Pag. 0-0 | ||||||
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Rezumat | ||||||
The object of the paper are the regular topological spaces X in which there exists a metric d related to the topology in the following way: for every nonempty open subset U of X and for every ε>0 there exists a nonempty open subset V of U with d-diameter less than ε. It is shown that such a space X is pseudo-almost Čech complete if, and only if, it contains a dense completely metrizable subset (X is pseudo-almost Čech complete if it is a subset of some pseudocompact space Y and contains as a dense subset some Gδ-subset of Y). A large class of spaces L is described (containing all Borel subsets of compact spaces, all pseudocompact spaces and all p-spaces of Arhangel'skii) such that, if X belongs to L and admits a metric d with the above property, then X is “metrizable up to a first Baire category subset”. I.e. X is the union of two sets X1 and X2 where X1 is of the first Baire category in X and X2 is metrizable. We provide also different characterizations of the class L. |
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Cuvinte-cheie Dense metrizable subset, Fragmentability of sets, Topological game, Winning strategyČech complete |
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