Weak continuity properties of topologized groups
MetadataShow full metadata
A topologized group is simply a group (G, ·) equipped with a topology t. The question as to when a topologized group (G, ·, t) is a topological group has been studied by many authors in the literature. In the recent work of A. V. Arhangel'skii and E. A. Reznichenko in 2005, and S. Ferri, S. Hernandez and T. S. Wu in 2006, certain types of weak continuity properties are employed either implicitly or explicitly. In this talk, I shall analyze various types of weak continuity properties of group operations. As an application, it is shown that if (G, ·, t) is a right (resp. left) semitopological group with a regular topology such that dev(G) < Nov(G) and all left (resp. right) translations are feebly continuous, then (G, ·, t) is a topological group.