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<identifier identifierType='DOI'>10.1016/j.topol.2019.107004</identifier>
<creators>
<creator>
<creatorName>Cioban, M.M.</creatorName>
<affiliation>Universitatea de Stat din Tiraspol, Moldova, Republica</affiliation>
</creator>
<creator>
<creatorName>Kenderov, P.</creatorName>
<affiliation>Institutul de Matematică şi Informatică al AŞ a Bulgariei, Bulgaria</affiliation>
</creator>
<creator>
<creatorName>Revalski, J.</creatorName>
<affiliation>Institutul de Matematică şi Informatică al AŞ a Bulgariei, Bulgaria</affiliation>
</creator>
</creators>
<titles>
<title xml:lang='en'>Fragmentability of open sets and topological games</title>
</titles>
<publisher>Instrumentul Bibliometric National</publisher>
<publicationYear>2020</publicationYear>
<relatedIdentifier relatedIdentifierType='ISSN' relationType='IsPartOf'>0166-8641</relatedIdentifier>
<subjects>
<subject>Baire category</subject>
<subject>Dense completely metrizable subset</subject>
<subject>Fragmentability of sets</subject>
<subject>Topological game</subject>
<subject>Winning strategy</subject>
</subjects>
<dates>
<date dateType='Issued'>2020-04-15</date>
</dates>
<resourceType resourceTypeGeneral='Text'>Journal article</resourceType>
<descriptions>
<description xml:lang='en' descriptionType='Abstract'><p>We give internal and external characterizations of the topological spaces X in which there exists a metric d (not necessarily generating the topology of X) which fragments the nonempty open sets. I.e. every nonempty open subset contains open subsets of arbitrarily small d-diameter. One of the characterizations says that every such space X is the union of two disjoint sets X<sub>1</sub> and X<sub>2</sub> where X<sub>1</sub> is of the first Baire category in X and X<sub>2</sub> admits a continuous one-to-one mapping into a metrizable space. An external characterization is obtained via the existence of a winning strategy for one of the players in a topological game similar to the Banach-Mazur game. An example of a space X is exhibited for which neither of the players in this game has a winning strategy. Of special interest is the case when the metric d which fragments the nonempty open sets of X is complete and generates a topology finer than the topology of X. This happens if and only if X contains a dense completely metrizable subset.</p></description>
</descriptions>
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<format>uri</format>
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