A criterion of the existence of an embedding of a monothetic monoid into a topological group (Q2316714)

This paper contribute toward the solving of the problem of embedding a topological semigroup into a topological group. While prior embedding construction benefit from the group of quotients of the given monoid, current paper uses unitary extension of this monoid where all its unitary Cauchy filters converge. The authors first study properties of unitary Cauchy filters on a monothetic monoid which are crucial for the constructive proof of the main embedding theorem. The main result (Theorem 2.2) states, that a monothetic monoid can be embedded into a topological group if and only if it is cancellative and its topology is \(T_3\) and non-viscous.