dc.contributor.author | Elliott, Luke | |
dc.contributor.author | Jonusas, Julius | |
dc.contributor.author | Mitchell, James D. | |
dc.contributor.author | Peresse, Yann | |
dc.contributor.author | Pinsker, Michael | |
dc.date.accessioned | 2023-12-08T10:45:01Z | |
dc.date.available | 2023-12-08T10:45:01Z | |
dc.date.issued | 2023-10-15 | |
dc.identifier.citation | Elliott , 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.issn | 0001-8708 | |
dc.identifier.uri | http://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.abstract | In 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 T(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.extent | 37 | |
dc.format.extent | 398756 | |
dc.language.iso | eng | |
dc.relation.ispartof | Advances in Mathematics | |
dc.subject | Semigroups | |
dc.subject | Topology | |
dc.subject | Group Theory | |
dc.subject | Combinatorics | |
dc.title | Polish topologies on endomorphism monoids of relational structures | en |
dc.contributor.institution | Mathematics and Theoretical Physics | |
dc.contributor.institution | School of Physics, Engineering & Computer Science | |
dc.contributor.institution | Department of Physics, Astronomy and Mathematics | |
dc.description.status | Peer reviewed | |
dc.date.embargoedUntil | 2025-08-03 | |
dc.identifier.url | https://arxiv.org/pdf/2203.11577.pdf | |
rioxxterms.versionofrecord | 10.1016/j.aim.2023.109214 | |
rioxxterms.type | Journal Article/Review | |
herts.preservation.rarelyaccessed | true | |