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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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