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dc.contributor.authorMesyan, Zak
dc.contributor.authorMitchell, James D.
dc.contributor.authorPeresse, Yann
dc.date.accessioned2021-02-19T15:15:02Z
dc.date.available2021-02-19T15:15:02Z
dc.date.issued2018-09-12
dc.identifier.citationMesyan , Z , Mitchell , J D & Peresse , Y 2018 ' Topological transformation monoids ' arXiv . < https://arxiv.org/abs/1809.04590 >
dc.identifier.otherPURE: 24663505
dc.identifier.otherPURE UUID: 1044f673-c0ec-4878-bf8e-b02a50190357
dc.identifier.urihttp://hdl.handle.net/2299/23926
dc.description© 2018 The Author(s).
dc.description.abstractWe investigate semigroup topologies on the full transformation monoid T(X) of an infinite set X. We show that the standard pointwise topology is the weakest Hausdorff semigroup topology on T(X), show that the pointwise topology is the unique Hausdorff semigroup topology on T(X) that induces the pointwise topology on the group of all permutations of X, and construct |X| distinct Hausdorff semigroup topologies on T(X). In the case where X is countable, we prove that the pointwise topology is the only Polish semigroup topology on T(X). We also show that every separable semigroup topology on T(X) is perfect, describe the compact sets in an arbitrary Hausdorff semigroup topology on T(X), and show that there are no locally compact perfect Hausdorff semigroup topologies on T(X) when |X| has uncountable cofinality.en
dc.language.isoeng
dc.publisherarXiv
dc.rightsOpen
dc.subjectSEMIGROUPS
dc.subjecttransformation semigroup
dc.subjectTopological Algebra
dc.titleTopological transformation monoidsen
dc.contributor.institutionMathematical and Theoretical Physics
dc.contributor.institutionSchool of Physics, Astronomy and Mathematics
dc.identifier.urlhttps://arxiv.org/abs/1809.04590
dc.description.versiontypeSubmitted Version
dcterms.dateAccepted2018-09-12
rioxxterms.versionSMUR
rioxxterms.licenseref.uriUnspecified
rioxxterms.typeWorking paper
herts.preservation.rarelyaccessedtrue
herts.rights.accesstypeOpen


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