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Remarks on the rings of functions which have a finite numb er of di scontinuities

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Remarks on the rings of functions which have a finite numb er of di scontinuities

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dc.contributor.author Ahmadi Zand, Mohammad Reza es_ES
dc.contributor.author Khosravi, Zahra es_ES
dc.date.accessioned 2021-04-16T09:06:17Z
dc.date.available 2021-04-16T09:06:17Z
dc.date.issued 2021-04-01
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/165247
dc.description.abstract [EN] Let X be an arbitrary topological space. F(X) denotes the set of all real-valued functions on X and C(X)F denotes the set of all f ∈ F(X) such that f is discontinuous at most on a finite set. It is proved that if r is a positive real number, then for any f ∈ C(X)F which is not a unit of C(X)F there exists g ∈ C(X)F such that g ≠ 1 and f = gr f. We show that every member of C(X)F is continuous on a dense open subset of X if and only if every non-isolated point of X is nowhere dense. It is shown that C(X)F is an Artinian ring if and only if the space X is finite. We also provide examples to illustrate the results presented herein. es_ES
dc.description.sponsorship Department of pure Mathematics Yazd university. We record our pleasure to the anonymous referee for his or her constructive report and many helpful suggestions on the main results of the earlier version of the manuscript which improved the presentation of the paper. es_ES
dc.language Inglés es_ES
dc.publisher Universitat Politècnica de València es_ES
dc.relation.ispartof Applied General Topology es_ES
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject C(X)F es_ES
dc.subject Z-ultrafilter es_ES
dc.subject Completely separated es_ES
dc.subject C(X)F -embedded es_ES
dc.subject Z-filter es_ES
dc.subject Over-rings of C(X) es_ES
dc.subject Artinian ring es_ES
dc.title Remarks on the rings of functions which have a finite numb er of di scontinuities es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.4995/agt.2021.14332
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Ahmadi Zand, MR.; Khosravi, Z. (2021). Remarks on the rings of functions which have a finite numb er of di scontinuities. Applied General Topology. 22(1):139-147. https://doi.org/10.4995/agt.2021.14332 es_ES
dc.description.accrualMethod OJS es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2021.14332 es_ES
dc.description.upvformatpinicio 139 es_ES
dc.description.upvformatpfin 147 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 22 es_ES
dc.description.issue 1 es_ES
dc.identifier.eissn 1989-4147
dc.relation.pasarela OJS\14332 es_ES
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dc.description.references R. Engelking, General Topology, Sigma Ser. Pure Math. 6, Heldermann-Verlag, Berlin, 1989. es_ES
dc.description.references Z. Gharabaghi, M. Ghirati. and A. Taherifar, On the rings of functions which are discontinuous on a finite set, Houston J. Math. 44, no. 2 (2018), 721-739. es_ES
dc.description.references L. Gillman and M. Jerison, Rings of Continuous Functions, Springer-Verlag, New York-Heidelberg, 1976. es_ES
dc.description.references N. Levine, Generalized closed sets in topology. Rend. Circ. Mat. Palermo. 19, no. 2 (1970), 89-96. https://doi.org/10.1007/BF02843888 es_ES


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