On topologies on the underlying set of a topological monoid induced by its unitary extensions

Abstract

Extensions of a given topological monoid where all its unitary Cauchy filters converge, can induce di˙erent topologies on its underlying set. We study properties of these topologies and prove a condition under which the initial topology of this monoid is one of them.

Keywords

• topological monoid
• cauchy filter
• completion
• 22a15
• 54h10