Brick decompositions and $Q$-manifolds

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 ${Q_0} = Q\backslash \;\text {point}\approx Q \times [0,1)$. Then $Y \times Q \approx |K| \times Q$ (respectively, $Y \times {Q_0} \approx |K| \times {Q_0}$).