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Extensions of closure spaces

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Extensions of closure spaces

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dc.contributor.author Deses, D. es_ES
dc.contributor.author de Groot-Van der Voorde, A. es_ES
dc.contributor.author Lowen-Colebunders, E. es_ES
dc.date.accessioned 2017-06-05T10:02:24Z
dc.date.available 2017-06-05T10:02:24Z
dc.date.issued 2003-10-01
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/82367
dc.description.abstract [EN] A closure space X is a set endowed with a closure operator P(X) → P(X), satisfying the usual topological axioms, except finite additivity. A T1 closure extension Y of a closure space X induces a structure ϒ on X satisfying the smallness axioms introduced by H. Herrlich [?], except the one on finite unions of collections. We'll use the word seminearness for a smallness structure of this type, i.e. satisfying the conditions (S1),(S2),(S3) and (S5) from [?]. In this paper we show that every T1 seminearness structure ϒ on X can in fact be induced by a T1 closure extension. This result is quite different from its topological counterpart which was treated by S.A. Naimpally and J.H.M. Whitfield in [?]. Also in the topological setting the existence of (strict) extensions satisfying higher separation conditions such as T2 and T3 has been completely characterized by means of concreteness, separatedness and regularity [?]. In the closure setting these conditions will appear to be too weak to ensure the existence of suitable (strict) extensions. In this paper we introduce stronger alternatives in order to present internal characterizations of the existence of (strict) T2 or strict regular closure extensions. 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 Closure space es_ES
dc.subject Seminearness es_ES
dc.subject Separation es_ES
dc.subject Regularity es_ES
dc.subject (strict) extension es_ES
dc.subject Minimal small stack es_ES
dc.title Extensions of closure spaces es_ES
dc.type Artículo es_ES
dc.date.updated 2017-06-05T09:13:39Z
dc.identifier.doi 10.4995/agt.2003.2028
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Deses, D.; De Groot-Van Der Voorde, A.; Lowen-Colebunders, E. (2003). Extensions of closure spaces. Applied General Topology. 4(2):223-241. doi:10.4995/agt.2003.2028. es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2003.2028 es_ES
dc.description.upvformatpinicio 223 es_ES
dc.description.upvformatpfin 241 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 4
dc.description.issue 2
dc.identifier.eissn 1989-4147
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