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Pointwise convergence on the rings of functions which are discontinuous on a set of measure zero

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Pointwise convergence on the rings of functions which are discontinuous on a set of measure zero

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dc.contributor.author Mandal, Dhananjoy es_ES
dc.contributor.author Singha, Achintya es_ES
dc.contributor.author Bag, Sagarmoy es_ES
dc.date.accessioned 2024-04-26T12:40:58Z
dc.date.available 2024-04-26T12:40:58Z
dc.date.issued 2024-04-02
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/203797
dc.description.abstract [EN] Consider the ring ℳ∘ ( X , μ ) of functions which are discontinuous on a set of measure zero which is introduced and studied extensively in [2]. In this paper, we have introduced a ring B1 ( X , μ ) of functions which are pointwise limits of sequences of functions in ℳ∘ ( X , μ ) . We have studied various properties of zero sets, B1 ( X , μ ) -separated and B1 ( X , μ ) -embedded subsets of B1 ( X , μ ) and also established an analogous version of Urysohn's extension theorem. We have investigated a connection between ideals of B1 ( X , μ ) and ZB -filters on X. We have studied an analogue of Gelfand-Kolmogoroff theorem in our setting. We have defined real maximal ideals of B1 ( X , μ ) and established the result | ℛ M a x ( ℳ∘ ( X , μ ) ) | = | ℛ M a x ( B1 ( X , μ ) ) | , where ℛ M a x ( ℳ∘ ( X , μ ) ) and ℛ M a x ( B1 ( X , μ ) ) are the sets of all real maximal ideals of ℳ∘ ( X , μ ) and B1 ( X , μ ) respectively. 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 - Compartir igual (by-nc-sa) es_ES
dc.subject Measure spaces es_ES
dc.subject Complete measure es_ES
dc.subject B1-separated es_ES
dc.subject ZB -filters es_ES
dc.subject B1(X,μ)-compact space es_ES
dc.subject Real maximal ideal es_ES
dc.title Pointwise convergence on the rings of functions which are discontinuous on a set of measure zero es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.4995/agt.2024.18884
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Mandal, D.; Singha, A.; Bag, S. (2024). Pointwise convergence on the rings of functions which are discontinuous on a set of measure zero. Applied General Topology. 25(1):253-275. https://doi.org/10.4995/agt.2024.18884 es_ES
dc.description.accrualMethod OJS es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2024.18884 es_ES
dc.description.upvformatpinicio 253 es_ES
dc.description.upvformatpfin 275 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 25 es_ES
dc.description.issue 1 es_ES
dc.identifier.eissn 1989-4147
dc.relation.pasarela OJS\18884 es_ES


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