A variation on arithmetic continuity

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dc.authorid0000-0001-7344-5826en_US
dc.contributor.authorCakalli, Huseyin
dc.date.accessioned2024-07-12T21:45:17Z
dc.date.available2024-07-12T21:45:17Z
dc.date.issued2017en_US
dc.departmentMaltepe Üniversitesien_US
dc.description.abstractA sequence (x(k)) of points R, the set of real numbers, is called arithmetically convergent if for each epsilon > 0 there is an lat for every integer m, we have vertical bar x(m) - x(<m,n>)vertical bar < epsilon, where k vertical bar n means that k divides n or n is a multiple of k, and the symbol < m, n > denotes the greatest common divisor of the integers m and n. We prove that a subset of R is bounded if and only if it is arithmetically compact, where a subset E of R is arithmetically compact if any sequence of point in E has an arithmetically convergent subsequence. It turns out that the set of arithmetically continuous functions on an arithmetically compact subset of R coincides with the set of uniformly continuous functions where a function f defined on a subset E of lit is arithmetically continuous if it preserves arithmetically convergent sequences, i.e., (f (x(n)) is arithmetically convergent whenever (x(n)) is an arithmetic convergent sequence of points in E.en_US
dc.identifier.doi10.5269/bspm.v35i3.29640
dc.identifier.endpage202en_US
dc.identifier.issn0037-8712
dc.identifier.issn2175-1188
dc.identifier.issue3en_US
dc.identifier.scopus2-s2.0-85010445005en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage195en_US
dc.identifier.urihttps://dx.doi.org/10.5269/bspm.v35i3.29640
dc.identifier.urihttps://hdl.handle.net/20.500.12415/7819
dc.identifier.volume35en_US
dc.identifier.wosWOS:000410613600013en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorCakalli, Huseyin
dc.language.isoenen_US
dc.publisherSOC PARANAENSE MATEMATICAen_US
dc.relation.ispartofBOLETIM SOCIEDADE PARANAENSE DE MATEMATICAen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.snmzKY00443
dc.subjectarithmetical convergent sequencesen_US
dc.subjectboundednessen_US
dc.subjectuniform continuityen_US
dc.titleA variation on arithmetic continuityen_US
dc.typeArticle
dspace.entity.typePublication

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