Action of convergence groups
by
Nandita Rath
University of Western Australia

Convergence spaces are generalisations of topological spaces. A group G with a compatible convergence structure is called a convergence group. An action of the convergence group G on a convergence space X is defined as an algebraic group action, which is also continuous. We will discuss a few examples of actions of convergence groups and new actions arising from an action of G on X. Attempts have been made to establish a homeomorphic representation of G on X in the special case when X is a limit space.

This is a preliminary observation on the actions of convergence groups, which extend some of the concepts involved in actions of toplogical groups without the restriction of compactness.

Date received: June 6, 2002