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On rings of real valued clopen continuous functions

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On rings of real valued clopen continuous functions

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dc.contributor.author Afrooz, Susan es_ES
dc.contributor.author Azarpanah, Fariborz es_ES
dc.contributor.author Etebar, Masoomeh es_ES
dc.date.accessioned 2018-10-05T07:11:57Z
dc.date.available 2018-10-05T07:11:57Z
dc.date.issued 2018-10-04
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/109446
dc.description.abstract [EN] Among variant kinds of strong continuity in the literature, the clopen continuity or cl-supercontinuity (i.e., inverse image of every open set is a union of clopen sets) is considered in this paper. We investigate and study the ring Cs(X) of all real valued clopen continuous functions on a topological space X. It is shown that every ƒ ∈ Cs(X) is constant on each quasi-component in X and using this fact we show that Cs(X) ≅ C(Y), where Y is a zero-dimensional s-quotient space of X. Whenever X is locally connected, we observe that Cs(X) ≅ C(Y), where Y is a discrete space. Maximal ideals of Cs(X) are characterized in terms of quasi-components in X and it turns out that X is mildly compact(every clopen cover has a finite subcover) if and only if every maximal ideal of Cs(X)is fixed. It is shown that the socle of Cs(X) is an essential ideal if and only if the union of all open quasi-components in X is s-dense. Finally the counterparts of some familiar spaces, such as Ps-spaces, almost Ps-spaces, s-basically and s-extremally disconnected spaces are defined and some algebraic characterizations of them are given via the ring Cs(X). es_ES
dc.description.sponsorship The authors would like to thank the referee for a carefulreading of this article. 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 Clopen continuous (cl-supercontinuous) es_ES
dc.subject Zero-dimensional es_ES
dc.subject Ps-space es_ES
dc.subject Almost Ps-space es_ES
dc.subject Baer ring es_ES
dc.subject p.p. ring es_ES
dc.subject Quasi-component es_ES
dc.subject Socle es_ES
dc.subject Mildly compact es_ES
dc.subject S-basically and s-extremally disconnected space es_ES
dc.title On rings of real valued clopen continuous functions es_ES
dc.type Artículo es_ES
dc.date.updated 2018-10-04T12:57:53Z
dc.identifier.doi 10.4995/agt.2018.7667
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Afrooz, S.; Azarpanah, F.; Etebar, M. (2018). On rings of real valued clopen continuous functions. Applied General Topology. 19(2):203-216. doi:10.4995/agt.2018.7667 es_ES
dc.description.accrualMethod SWORD es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2018.7667 es_ES
dc.description.upvformatpinicio 203 es_ES
dc.description.upvformatpfin 216 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 19
dc.description.issue 2
dc.identifier.eissn 1989-4147
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