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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On infinite-dimensional manifold triples

Authors: Katsuro Sakai and Raymond Y. Wong
Journal: Trans. Amer. Math. Soc. 318 (1990), 545-555
MSC: Primary 57N20; Secondary 58B99
MathSciNet review: 994171
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Abstract: Let $ Q$ denote the Hilbert cube $ {[ - 1,1]^\omega },\;s = {( - 1,1)^\omega }$ the pseudo-interior of $ Q,\;\Sigma = \{ ({x_i}) \in s\vert\sup \vert{x_i}\vert < 1\} $ and $ \sigma = \{ ({x_i}) \in s\vert{x_i} = 0\;{\text{except for finitely many}}\;i\} $. A triple $ (X,M,N)$ of separable metrizable spaces is called a $ (Q,\Sigma ,\sigma )$- (or $ (s,\Sigma ,\sigma )$-)manifold triple if it is locally homeomorphic to $ (Q,\Sigma ,\sigma )$ (or $ (s,\Sigma ,\sigma )$). In this paper, we study such manifold triples and give some characterizations.

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PII: S 0002-9947(1990)0994171-4
Keywords: $ (Q,\Sigma ,\sigma )$-manifold triple, $ (s,\Sigma ,\sigma )$-manifold triple, (f.d.) cap pair, cap manifold pair
Article copyright: © Copyright 1990 American Mathematical Society