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dc.contributor.authorElliott, Luke
dc.contributor.authorJonusas, Julius
dc.contributor.authorMitchell, James D.
dc.contributor.authorPeresse, Yann
dc.contributor.authorPinsker, Michael
dc.date.accessioned2023-12-08T10:45:01Z
dc.date.available2023-12-08T10:45:01Z
dc.date.issued2023-10-15
dc.identifier.citationElliott , L , Jonusas , J , Mitchell , J D , Peresse , Y & Pinsker , M 2023 , ' Polish topologies on endomorphism monoids of relational structures ' , Advances in Mathematics , vol. 431 , 109214 , pp. 1-37 . https://doi.org/10.1016/j.aim.2023.109214
dc.identifier.issn0001-8708
dc.identifier.urihttp://hdl.handle.net/2299/27269
dc.description© 2023 Elsevier Inc. All rights reserved. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1016/j.aim.2023.109214
dc.description.abstractIn this paper we present general techniques for characterising minimal and maximal semigroup topologies on the endomorphism monoid End(A) of a countable relational structure A. As applications, we show that the endomorphism monoids of several well-known relational structures, including the random graph, the random directed graph, and the random partial order, possess a unique Polish semigroup topology. In every case this unique topology is the subspace topology induced by the usual topology on the Baire space N N. We also show that many of these structures have the property that every homomorphism from their endomorphism monoid to a second countable topological semigroup is continuous; referred to as automatic continuity. Many of the results about endomorphism monoids are extended to clones of polymorphisms on the same structures.en
dc.format.extent37
dc.format.extent398756
dc.language.isoeng
dc.relation.ispartofAdvances in Mathematics
dc.subjectSemigroups
dc.subjectTopology
dc.subjectGroup Theory
dc.subjectCombinatorics
dc.subjectAutomatic continuity
dc.subjectReconstruction
dc.subjectEndomorphism monoid
dc.subjectPointwise convergence topology
dc.subjectPolish topology
dc.subjectGeneral Mathematics
dc.titlePolish topologies on endomorphism monoids of relational structuresen
dc.contributor.institutionMathematics and Theoretical Physics
dc.contributor.institutionSchool of Physics, Engineering & Computer Science
dc.contributor.institutionDepartment of Physics, Astronomy and Mathematics
dc.description.statusPeer reviewed
dc.date.embargoedUntil2025-08-03
dc.identifier.urlhttp://www.scopus.com/inward/record.url?scp=85174926254&partnerID=8YFLogxK
dc.identifier.urlhttps://arxiv.org/pdf/2203.11577.pdf
rioxxterms.versionofrecord10.1016/j.aim.2023.109214
rioxxterms.typeJournal Article/Review
herts.preservation.rarelyaccessedtrue


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