International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 371-378

On G-finitistic spaces and related notions

Satya Deo1 and Janak Singh Andotra2

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.


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.