Combinatorial characterization of pseudometrics

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dc.contributor.author Dovgoshey, O.
dc.contributor.author Luukkainen, J.
dc.date.accessioned 2020-07-02T11:42:01Z
dc.date.available 2020-07-02T11:42:01Z
dc.date.issued 2020-06
dc.identifier.citation Dovgoshey , O & Luukkainen , J 2020 , ' Combinatorial characterization of pseudometrics ' , Acta Mathematica Hungarica , vol. 161 , no. 1 , pp. 257-291 . https://doi.org/10.1007/s10474-020-01020-x
dc.identifier.other PURE: 129757431
dc.identifier.other PURE UUID: 17f90cfe-6f6a-479b-9ae3-08243af792c4
dc.identifier.other WOS: 000540146900012
dc.identifier.other ORCID: /0000-0001-5230-1268/work/93118167
dc.identifier.uri http://hdl.handle.net/10138/317289
dc.description.abstract Let X, Y be sets and let similar to, similar to be mappings with the domains X2 and Y 2 respectively. We say that similar to is combinatorially similar to similar to if there are bijections f : similar to(X2) similar to similar to(Y 2) and g : Y similar to X such that similar to (x, y) = f(similar to(g(x), g(y))) for all x, y similar to Y. It is shown that the semigroups of binary relations generated by sets {similar to-1 (a): a similar to similar to(X 2)} and {similar to-1 (b): b similar to similar to(Y 2)} are isomorphic for combinatorially similar similar to and similar to. The necessary and sufficient conditions under which a given mapping is combinatorially similar to a pseudometric, or strongly rigid pseudometric, or discrete pseudometric are found. The algebraic structure of semigroups generated by {d-1 (r): r similar to d(X 2)} is completely described for nondiscrete, strongly rigid pseudometrics and, also, for discrete pseudometrics d: X2 similar to R. en
dc.format.extent 35
dc.language.iso eng
dc.relation.ispartof Acta Mathematica Hungarica
dc.rights.uri info:eu-repo/semantics/openAccess
dc.subject 111 Mathematics
dc.subject pseudometric
dc.subject strongly rigid metric
dc.subject equivalence relation
dc.subject semigroup
dc.subject of binary relations
dc.title Combinatorial characterization of pseudometrics en
dc.type Article
dc.contributor.organization Department of Mathematics and Statistics
dc.description.reviewstatus Peer reviewed
dc.relation.doi https://doi.org/10.1007/s10474-020-01020-x
dc.relation.issn 0236-5294
dc.rights.accesslevel openAccess
dc.type.version acceptedVersion
dc.identifier.url https://arxiv.org/abs/1906.07411

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