Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A $ Q$-manifold local-compactification of a metric combinatorial $ \infty$-manifold

Author: Katsuro Sakai
Journal: Proc. Amer. Math. Soc. 100 (1987), 775-780
MSC: Primary 57N20; Secondary 54E45, 54F40, 57Q15
MathSciNet review: 894453
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Abstract: Let $ K$ be a combinatorial $ \infty $-manifold, that is, a countable simplicial complex such that the star of each vertex is combinatorially equivalent to the countable-infinite full simplicial complex. Then the space $ {\left\vert K \right\vert _m}$ with the metric topology is a manifold modeled on the space $ \sigma $, where $ \sigma $ is the subspace of the Hilbert cube $ Q = {I^\omega }$ which consists of all points having at most finitely many nonzero coordinates. In this paper, we give a local-compactification of $ {\left\vert K \right\vert _m}$ which is a $ [0,1)$-stable $ Q$-manifold containing $ {\left\vert K \right\vert _m}$ as an f.d. cap set.

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Keywords: Simplicial complex, combinatorial $ \infty $-manifold, metric topology, localcompactification, $ \sigma $-manifold, $ Q$-manifold, $ [0,1)$-stable, f.d. cap set, $ Z$-set, ANR
Article copyright: © Copyright 1987 American Mathematical Society