@CAT Tuesday March 27, 2012 2:30-3:30 Colloquium Room Gabor Lukacs Automatic continuity and open mapping theorems of topological algebras ABSTRACT: There are a number of interesting results in the literature stating that certain algebraic and/or set-theoretic conditions on a map imply the continuity of a map or its inverse. A few prominent examples are: 1. every group homomorphism of SO(3,R) into a compact group is continuous; 2. every bounded linear operation from a Banach space onto a Banach space is open; 3. every *-homomorphism of C^*-algebras is continuous; 4. every continuous homomorphism from the group Z equipped with the p-adic topology is open onto its image. In this talk, we survey results of this nature, and present a solution to the problem posed by Jeff Egger a few weeks ago concerning continuous homomorphisms of locally compact abelian groups that preserve null sets (a.k.a. Wendt maps). How the term is winding down: April 3, Dorette Pronk