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On cardinalities and compact closures

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On cardinalities and compact closures

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dc.contributor.author Krebs, Mike es_ES
dc.date.accessioned 2017-04-19T12:07:30Z
dc.date.available 2017-04-19T12:07:30Z
dc.date.issued 2017-04-03
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/79818
dc.description.abstract [EN] We show that there exists a Hausdorff topology on the set R of real numbers such that a subset A of R has compact closure if and only if A is countable. More generally, given any set X and any infinite set S, we prove that there exists a Hausdorff topology on X such that a subset A of X has compact closure if and only if the cardinality of A is less than or equal to that of S. When we attempt to replace “than than or equal to” in the preceding statement with “strictly less than,” the situation is more delicate; we show that the theorem extends to this case when S has regular cardinality but can fail when it does not. This counterexample shows that not every bornology is a bornology of compact closure. These results lie in the intersection of analysis, general topology, and set theory. es_ES
dc.language Inglés es_ES
dc.publisher Universitat Politècnica de València
dc.relation.ispartof Applied General Topology
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Bornology es_ES
dc.subject Topology es_ES
dc.subject Hausdorff cardinality es_ES
dc.subject Compact closure es_ES
dc.title On cardinalities and compact closures es_ES
dc.type Artículo es_ES
dc.date.updated 2017-04-19T11:19:59Z
dc.identifier.doi 10.4995/agt.2017.6376
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Krebs, M. (2017). On cardinalities and compact closures. Applied General Topology. 18(1):107-115. doi:10.4995/agt.2017.6376. es_ES
dc.description.accrualMethod SWORD es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2017.6376 es_ES
dc.description.upvformatpinicio 107 es_ES
dc.description.upvformatpfin 115 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 18
dc.description.issue 1
dc.identifier.eissn 1989-4147
dc.description.references H. Hogbe-Nlend, Bornologies and functional analysis, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. es_ES


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