Box Topologies
Definition
Given a family of topological spaces
$\mathcal{F} = \set{(X_\alpha ,
\mathcal{T} _\alpha }_{\alpha \in I}$, the
box topology of
$\mathcal{F} $ is the topology on $X =
\prod_{\alpha \in I} X_\alpha $ generated by the
set
\[
\Set*{ \prod_{\alpha \in I} U_i }{ U_\alpha \in
\mathcal{T} _\alpha }
\]