Canonical topologies for monoids

Abstract: The problem of determining which topologies are compatible with the multiplication and inversion in a group has an extensive history that can be traced back to Markov. For example, it has been shown by Gaughan in the 1960s that the symmetric group on a countable set has a unique Polish topology which makes composition and inversion continuous. In the same way we will explore to what extent the algebraic structure of a monoid structure determines the topologies which make the multiplication of the monoid continuous, such topologies are known as semigroup topologies. In particular, we will investigate which monoids have a unique Polish semigroup topology and which have automatic continuity. If M is a monoid equipped with a semigroup topology, then automatic continuity, in this context, means that every homomorphsim from M to a second countable topological monoid is necessarily continuous.

operator algebrasrings and algebras

Audience: researchers in the topic

Western Sydney University Abend Seminars

Series comments: Description: Western Sydney University Abend Seminars

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