Conţinutul numărului revistei |
Articolul precedent |
Articolul urmator |
518 0 |
SM ISO690:2012 CHOBAN, Mitrofan, KENDEROV, Petar, REVALSKI, Julian Petrov. Fragmentability of open sets and topological games. In: Topology and its Applications, 2020, nr. 275, p. 0. ISSN 0166-8641. DOI: https://doi.org/10.1016/j.topol.2019.107004 |
EXPORT metadate: Google Scholar Crossref CERIF DataCite Dublin Core |
Topology and its Applications | ||||||
Numărul 275 / 2020 / ISSN 0166-8641 | ||||||
|
||||||
DOI:https://doi.org/10.1016/j.topol.2019.107004 | ||||||
Pag. 0-0 | ||||||
|
||||||
Rezumat | ||||||
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 X1 and X2 where X1 is of the first Baire category in X and X2 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. |
||||||
Cuvinte-cheie Baire category, Dense completely metrizable subset, Fragmentability of sets, Topological game, Winning strategy |
||||||
|
Cerif XML Export
<?xml version='1.0' encoding='utf-8'?> <CERIF xmlns='urn:xmlns:org:eurocris:cerif-1.5-1' xsi:schemaLocation='urn:xmlns:org:eurocris:cerif-1.5-1 http://www.eurocris.org/Uploads/Web%20pages/CERIF-1.5/CERIF_1.5_1.xsd' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' release='1.5' date='2012-10-07' sourceDatabase='Output Profile'> <cfResPubl> <cfResPublId>ibn-ResPubl-111684</cfResPublId> <cfResPublDate>2020-04-15</cfResPublDate> <cfIssue>275</cfIssue> <cfISSN>0166-8641</cfISSN> <cfURI>https://ibn.idsi.md/ro/vizualizare_articol/111684</cfURI> <cfTitle cfLangCode='EN' cfTrans='o'>Fragmentability of open sets and topological games</cfTitle> <cfKeyw cfLangCode='EN' cfTrans='o'>Baire category; Dense completely metrizable subset; Fragmentability of sets; Topological game; Winning strategy</cfKeyw> <cfAbstr cfLangCode='EN' cfTrans='o'><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></cfAbstr> <cfResPubl_Class> <cfClassId>eda2d9e9-34c5-11e1-b86c-0800200c9a66</cfClassId> <cfClassSchemeId>759af938-34ae-11e1-b86c-0800200c9a66</cfClassSchemeId> <cfStartDate>2020-04-15T24:00:00</cfStartDate> </cfResPubl_Class> <cfResPubl_Class> <cfClassId>e601872f-4b7e-4d88-929f-7df027b226c9</cfClassId> <cfClassSchemeId>40e90e2f-446d-460a-98e5-5dce57550c48</cfClassSchemeId> <cfStartDate>2020-04-15T24:00:00</cfStartDate> </cfResPubl_Class> <cfPers_ResPubl> <cfPersId>ibn-person-52</cfPersId> <cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId> <cfClassSchemeId>b7135ad0-1d00-11e1-8bc2-0800200c9a66</cfClassSchemeId> <cfStartDate>2020-04-15T24:00:00</cfStartDate> </cfPers_ResPubl> <cfPers_ResPubl> <cfPersId>ibn-person-54087</cfPersId> <cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId> <cfClassSchemeId>b7135ad0-1d00-11e1-8bc2-0800200c9a66</cfClassSchemeId> <cfStartDate>2020-04-15T24:00:00</cfStartDate> </cfPers_ResPubl> <cfPers_ResPubl> <cfPersId>ibn-person-81758</cfPersId> <cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId> <cfClassSchemeId>b7135ad0-1d00-11e1-8bc2-0800200c9a66</cfClassSchemeId> <cfStartDate>2020-04-15T24:00:00</cfStartDate> </cfPers_ResPubl> <cfFedId> <cfFedIdId>ibn-doi-111684</cfFedIdId> <cfFedId>10.1016/j.topol.2019.107004</cfFedId> <cfStartDate>2020-04-15T24:00:00</cfStartDate> <cfFedId_Class> <cfClassId>31d222b4-11e0-434b-b5ae-088119c51189</cfClassId> <cfClassSchemeId>bccb3266-689d-4740-a039-c96594b4d916</cfClassSchemeId> </cfFedId_Class> <cfFedId_Srv> <cfSrvId>5123451</cfSrvId> <cfClassId>eda2b2e2-34c5-11e1-b86c-0800200c9a66</cfClassId> <cfClassSchemeId>5a270628-f593-4ff4-a44a-95660c76e182</cfClassSchemeId> </cfFedId_Srv> </cfFedId> </cfResPubl> <cfPers> <cfPersId>ibn-Pers-52</cfPersId> <cfPersName_Pers> <cfPersNameId>ibn-PersName-52-3</cfPersNameId> <cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId> <cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId> <cfStartDate>2020-04-15T24:00:00</cfStartDate> <cfFamilyNames>Choban</cfFamilyNames> <cfFirstNames>Mitrofan</cfFirstNames> <cfFamilyNames>Чобан</cfFamilyNames> <cfFirstNames>Митрофан</cfFirstNames> </cfPersName_Pers> </cfPers> <cfPers> <cfPersId>ibn-Pers-54087</cfPersId> <cfPersName_Pers> <cfPersNameId>ibn-PersName-54087-3</cfPersNameId> <cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId> <cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId> <cfStartDate>2020-04-15T24:00:00</cfStartDate> <cfFamilyNames>Kenderov</cfFamilyNames> <cfFirstNames>Petar</cfFirstNames> </cfPersName_Pers> </cfPers> <cfPers> <cfPersId>ibn-Pers-81758</cfPersId> <cfPersName_Pers> <cfPersNameId>ibn-PersName-81758-3</cfPersNameId> <cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId> <cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId> <cfStartDate>2020-04-15T24:00:00</cfStartDate> <cfFamilyNames>Revalski</cfFamilyNames> <cfFirstNames>Julian Petrov</cfFirstNames> </cfPersName_Pers> </cfPers> <cfSrv> <cfSrvId>5123451</cfSrvId> <cfName cfLangCode='en' cfTrans='o'>CrossRef DOI prefix service</cfName> <cfDescr cfLangCode='en' cfTrans='o'>The service of issuing DOI prefixes to publishers</cfDescr> <cfKeyw cfLangCode='en' cfTrans='o'>persistent identifier; Digital Object Identifier</cfKeyw> </cfSrv> </CERIF>