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On $$G$$-finitistic spaces and related notions. (English) Zbl 0796.54015
Summary: 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 [the first author with Tej Bahadur Singh, J. Lond. Math. Soc., II. Ser. 25, 162-170 (1982; Zbl 0451.57019)] 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.
##### MSC:
 54B17 Adjunction spaces and similar constructions in general topology 54F45 Dimension theory in general topology
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