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SUMMARY:Julius Jonusas (Vienna)
DTSTART:20201029T090000Z
DTEND:20201029T100000Z
DTSTAMP:20260419T060542Z
UID:CRMDS/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CRMDS/24/">C
 anonical topologies for monoids</a>\nby Julius Jonusas (Vienna) as part of
  Western Sydney University Abend Seminars\n\n\nAbstract\nThe problem of de
 termining which topologies are compatible with the multiplication and inve
 rsion in a group has an extensive history that can be traced back to Marko
 v. For example\, it has been shown by Gaughan in the 1960s that the symmet
 ric group on a countable set has a unique Polish topology which makes comp
 osition and inversion continuous. In the same way we will explore to what 
 extent the algebraic structure of a monoid structure determines the topolo
 gies which make the multiplication of the monoid continuous\, such topolog
 ies are known as semigroup topologies. In particular\, we will investigate
  which monoids have a unique Polish semigroup topology and which have auto
 matic continuity. If M is a monoid equipped with a semigroup topology\, th
 en automatic continuity\, in this context\, means that every homomorphsim 
 from M to a second countable topological monoid is necessarily continuous.
 \n
LOCATION:https://researchseminars.org/talk/CRMDS/24/
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