We introduce the notion of stability of continuous homomorphisms of topological groups with respect to the compact-open topology on the space of all continuous functions between them and prove that the characters of any locally compact abelian group are stable in this sense. Using this notion we also generalize a global stability result on continuous homomorphisms between compact groups to a lo...

Hausdorff Abelian groups, Pontryagin duality and the principal.These notes provide a brief introduction to topological groups with a pdws pdf special. Charactres and Pontryagin-van Kampen duality to number theory, physics and. These notes provide a brief introduction to topological groups with a special. Section 7 is peacebuilding pdf dedicated to Pontryagin-van Kampen duality.We offer an eleme...

We shall prove the following theorem concerning compact connected abelian groups: For any element x in a compact connected abelian group there is an element y such that the closure of the cyclic group generated by y is connected and contains x. This is a generalisation of the well known fact that any compact connected group whose topology admits a basis of at most continuum cardinality is monot...