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• W2043054826 abstract "Let if be a combinatorial oo-manifold, that is, a countable sim- plicial complex such that the star of each vertex is combinatorially equivalent to the countable-infinite full simplicial complex. Then the space Km with the metric topology is a manifold modeled on the space o, where a is the subspace of the Hubert cube Q = Iu which consists of all points having at most finitely many nonzero coordinates. In this paper, we give a local-compactification of Km which is a (0, l)-stable Q-manifold containing Km as an f.d. cap set. 0. Introduction. Let X be a metric space with a metric ci. A closed subset A of X is called a Z-set in X if for each e > 0 and each map / : In —► X, n e N, there is a map j:/->Xi with d(f, g) 0, each m e N, and each finite-dimensional compact subset A of X, there is an n e N and an embedding h : A —> Mn such that hA n Mm = id and d(h, id) < e (An and Chi). Let a denote the subspace of the Hubert cube Q = Iu which consists of all points having at most finitely many nonzero coordinates. R. D. Anderson (An) showed that a is an f.d. cap set for Q and that for any f.d. cap set M for Q there is a homeomorphism of Q onto itself taking M onto a. A Hubert cube manifold (or Q-manifold) is a separable manifold modeled on the Hubert cube Q. A separable manifold modeled on the space a is called a a-manifold. T. A. Chapman (Chi) proved that any f.d. cap set for a Q-manifold is a er-manifold and any cr-manifold can be embedded as an f.d. cap set for a Q-manifold and that for any f.d. cap sets M and N for a Q-manifold X, there is a homeomorphism of X onto itself taking M onto N. Two simplicial complexes are said to be combinatorially equivalent provided they admit simplicially isomorphic subdivisions. A combinatorial oo-manifold is a countable simplicial complex such that the star of each vertex is combinatorially equivalent to the countable-infinite full simplicial complex, namely a co-simplex (Sai). For a simplicial complex K, K denotes the underlying set and Km denotes the space |JRT| with the topology induced by the metric di(x,y) = ^2 x(vi ~y(v)l v€K°" @default.
• W2043054826 created "2016-06-24" @default.
• W2043054826 creator A5084348228 @default.
• W2043054826 date "1987-04-01" @default.
• W2043054826 modified "2023-09-24" @default.
• W2043054826 title "A $Q$-manifold local-compactification of a metric combinatorial $infty$-manifold" @default.
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• W2043054826 doi "https://doi.org/10.1090/s0002-9939-1987-0894453-6" @default.
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