International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 371-378
doi:10.1155/S0161171292000486
On G-finitistic spaces and related notions
1Department of Mathematics and Computer Science, R.D. University, Jabalpur 482001, India
2Department of Mathematics, University of Jammu, Jammu 180001, India
Received 7 September 1988; Revised 12 December 1990
Copyright © 1992 Satya Deo and Janak Singh Andotra. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let X be a G-space where G is a topological group. We show that X is G-finitistic iff the orbit space X/G is finitistic. This result allows us to answer a question raised in [5] asking for an equivariant characterization of a non-finitistic G-space where G is a compact Lie group. For an arbitrary compact group G a simple characterization of G-finitistic spaces has been obtained in terms of new notions of G-compactness and G-dimension.