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Metric spaces related to Abelian groups

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Metric spaces related to Abelian groups

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dc.contributor.author Veisi, Amir es_ES
dc.contributor.author Delbaznasab, Ali es_ES
dc.date.accessioned 2021-04-16T09:11:44Z
dc.date.available 2021-04-16T09:11:44Z
dc.date.issued 2021-04-01
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/165250
dc.description.abstract [EN] When working with a metric space, we are dealing with the additive group (R, +). Replacing (R, +) with an Abelian group (G, ∗), offers a new structure of a metric space. We call it a G-metric space and the induced topology is called the G-metric topology. In this paper, we are studying G-metric spaces based on L-groups (i.e., partially ordered groups which are lattices). Some results in G-metric spaces are obtained. The G-metric topology is defined which is further studied for its topological properties. We prove that if G is a densely ordered group or an infinite cyclic group, then every G-metric space is Hausdorff. It is shown that if G is a Dedekind-complete densely ordered group, (X, d) a G-metric space, A ⊆ X and d is bounded, then f : X → G with f(x) = d(x, A) := inf{d(x, a) : a ∈ A} is continuous and further x ∈ clXA if and only if f(x) = e (the identity element in G). Moreover, we show that if G is a densely ordered group and further a closed subset of R, K(X) is the family of nonempty compact subsets of X, e < g ∈ G and d is bounded, then d′ (A, B) < g if and only if A ⊆ Nd(B, g) and B ⊆ Nd(A, g), where Nd(A, g) = {x ∈ X : d(x, A) < g}, dB(A) = sup{d(a, B) : a ∈ A} and d′ (A, B) = sup{dA(B), dB(A)}. es_ES
dc.description.sponsorship The authors are grateful to the referee for providing helpful comments and recommendations to improve the quality 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 G-metric space es_ES
dc.subject L-group es_ES
dc.subject Dedekind-complete group es_ES
dc.subject Densely ordered group es_ES
dc.subject Continuity es_ES
dc.title Metric spaces related to Abelian groups es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.4995/agt.2021.14446
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Veisi, A.; Delbaznasab, A. (2021). Metric spaces related to Abelian groups. Applied General Topology. 22(1):169-181. https://doi.org/10.4995/agt.2021.14446 es_ES
dc.description.accrualMethod OJS es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2021.14446 es_ES
dc.description.upvformatpinicio 169 es_ES
dc.description.upvformatpfin 181 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\14446 es_ES


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