On 𝑅^{∞}(𝑄^{∞})-manifold bundles over CW complexes

Liem, Vo Thanh

doi:10.1090/S0002-9947-1986-0854085-6

On $\textbf {R}^ \infty \;(Q^ \infty )$-manifold bundles over CW complexes
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Trans. Amer. Math. Soc. 297 (1986), 563-585 Request permission

Abstract:

Let $\Lambda \in \mathcal {C}\mathcal {W}(\mathcal {C}) \cup \mathcal {C}\mathcal {W}(\mathcal {M})$ be a pseudo CW complex generated either by Hausdorff compact spaces or by metric spaces. In the theory of manifolds modeled on ${R^\infty }$ or ${Q^\infty }$, we will prove the $\Lambda$-fiber-preserving versions of the following: Equivalences among the notions of $D$-sets, ${D^{\ast }}$-sets and infinite deficient sets; relative stability theorems; relative deformation of homotopy equivalences to homeomorphisms; strong unknotting theorem for $D$-embeddings; and $\alpha$-approximation theorems.

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