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 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.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.subject | Automatic continuity | |
dc.subject | Reconstruction | |
dc.subject | Endomorphism monoid | |
dc.subject | Pointwise convergence topology | |
dc.subject | Polish topology | |
dc.subject | General Mathematics | |
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 | http://www.scopus.com/inward/record.url?scp=85174926254&partnerID=8YFLogxK | |
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 | |