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Proceedings of the American Mathematical Society

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

 

 

Brick decompositions and $ Q$-manifolds


Authors: D. W. Curtis and G. Kozlowski
Journal: Proc. Amer. Math. Soc. 72 (1978), 170-174
MSC: Primary 57-XX
DOI: https://doi.org/10.1090/S0002-9939-1978-0503555-X
MathSciNet review: 503555
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Abstract: A brick decomposition (respectively, generalized brick decomposition) of a metric space Y is a locally finite, star-finite closed cover $ \{ {Y_\alpha }\} $ such that each nonempty intersection $ {Y_{{\alpha _1}}} \cap \cdots \cap {Y_{{\alpha _n}}},n \geqslant 1$, is a compact AR (respectively, locally compact AR). Let K be the nerve of the decomposition $ \{ {Y_\alpha }\} $, let Q be the Hilbert cube, and $ {Q_0} = Q\backslash\;$point$ \approx Q \times [0,1)$. Then $ Y \times Q \approx \vert K\vert \times Q$ (respectively, $ Y \times {Q_0} \approx \vert K\vert \times {Q_0}$).


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DOI: https://doi.org/10.1090/S0002-9939-1978-0503555-X
Keywords: Brick decomposition, nerve of a cover, simple homotopy type, Q-manifold
Article copyright: © Copyright 1978 American Mathematical Society