On G-finitistic spaces and related notions

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.

Keywords

• G-space
• finitistic space
• G-finitistic spaces
• compact Lie group and covering dimension.