Abstract
It is proved that a based-free action α of a given compact Lie groupG on the Hilbert cubeQ is equivalent to the standard based-free action σ if and only if the orbit spaceQ 0/α of the free partQ 0=Q* is aQ-manifold having the proper homotopy type of the orbit spaceQ 0/σ. The existence of an equivariant retraction (Q 0, σ)→(Q 0, α) is established. It is proved that for any TikhonovG-spaceX the family of all equivariant mapsX→ conG separates the points and the closed sets inX.
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Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 163–174, February, 1999.
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Antonyan, S.A. On based-free actions of compact lie groups on the hilbert cube. Math Notes 65, 135–143 (1999). https://doi.org/10.1007/BF02679809
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DOI: https://doi.org/10.1007/BF02679809