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Some homotopy properties of the homeomorphism groups of $ {\bf R}\sp \infty$ $ (Q\sp \infty)$-manifolds

Author: Vo Thanh Liem
Journal: Proc. Amer. Math. Soc. 100 (1987), 169-174
MSC: Primary 54C20; Secondary 54C35, 54C55
MathSciNet review: 883423
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Abstract: In this note we will prove that, given an $ {R^\infty }({Q^\infty })$-manifold $ M$, there is a deformation of $ \operatorname{Homo}(M)$ into $ \operatorname{Homeo}(M)$ whose final stage is a weak homotopy equivalence, and that if $ M$ has the homotopy type of a finite simplicial complex, then $ \operatorname{Homeo}(M)$ is an $ \operatorname{ANE}(\mathcal{C}\mathcal{W}(\mathcal{M}))$ and an $ \operatorname{ANE}(\mathcal{C}\mathcal{W}(\mathcal{C}),{G_\delta })$.

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Keywords: Homotopy, $ k$-space, evaluation map, fiber-preserving map
Article copyright: © Copyright 1987 American Mathematical Society

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