Abstract.One of the popular settings for group action is the category of groups. However, if we blend in the notion of continuity with the study of action, it is even more appreciated with applications in topological dynamics. A continuous action of a convergence group G on a convergence space X is well known [13]. In this case, X is called aG-space. In this paper, we study the group actions preserved by various convergence structures such as the quotient structure on the coset space. Also, attempts have been made to show that a few modifications of a G-space preserve the continuous group action.

Received: September 16, 2008

AMS Subject Classification: 54A20, 54B15, 57S05, 57S25, 22F05

Key Words and Phrases: convergence group, homeomorphism group, continuous group action, coset space, modifications of convergence structures

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 48
Issue: 3