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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On $ {\bf R}\sp \infty\;(Q\sp \infty)$-manifold bundles over CW complexes

Author: Vo Thanh Liem
Journal: Trans. Amer. Math. Soc. 297 (1986), 563-585
MSC: Primary 57N20; Secondary 57N35
MathSciNet review: 854085
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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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Keywords: Collar, invertible isotopy, stability theorem, infinite deficiency, direct limit space, weak topology, $ {G_\delta }$-set, unknotting theorem, fiber bundle
Article copyright: © Copyright 1986 American Mathematical Society