A brick decomposition (respectively, generalized brick decomposition) of a metric space Y is a locally finite, star-finite closed cover
{
Y
α
}
\{ {Y_\alpha }\}
such that each nonempty intersection
Y
α
1
∩
⋯
∩
Y
α
n
,
n
⩾
1
{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
α
}
\{ {Y_\alpha }\}
, let Q be the Hilbert cube, and
Q
0
=
Q
∖
point
≈
Q
×
[
0
,
1
)
{Q_0} = Q\backslash \;\text {point}\approx Q \times [0,1)
. Then
Y
×
Q
≈
|
K
|
×
Q
Y \times Q \approx |K| \times Q
(respectively,
Y
×
Q
0
≈
|
K
|
×
Q
0
Y \times {Q_0} \approx |K| \times {Q_0}
).