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Classification of $$G$$-spaces. (English. Russian original) Zbl 0812.57024
Russ. Acad. Sci., Izv., Math. 41, No. 3, 581-591 (1993); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 56, No. 6, 1345-1357 (1992).
A complete solution is given of a problem due to R. S. Palais [The classification of $$G$$-spaces, Mem. Am. Math. Soc. 36 (1960; Zbl 0119.384)]. Namely, it is proved that for every compact group $$G$$, the equivariant Hilbert cube is an $$n$$-universal $$G$$-space, for every $$n$$.
##### MSC:
 57S10 Compact groups of homeomorphisms 57S15 Compact Lie groups of differentiable transformations 55R35 Classifying spaces of groups and $$H$$-spaces in algebraic topology 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) 54F45 Dimension theory in general topology 57N20 Topology of infinite-dimensional manifolds
Zbl 0119.384
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