View source for Box topology

{{Stub page|grade=B|msg=Not that important because we have the product topology page, however it should be a slightly bigger stub page!}}
==Definition==
Let {{M|\big((X_\alpha,\mathcal{J}_\alpha)\big)_{\alpha\in I} }} be an arbitrary family of [[topological spaces]]. The ''box topology'' is the [[topology generated by]] the following {{link|basis|topology}}{{rITTMJML}}:
* {{M|1=\mathcal{B}:=\{\prod_{\alpha\in I}U_\alpha\ \vert\ (U_\alpha)_{\alpha\in I}\in\prod_{\alpha\in I}\mathcal{J}_\alpha\} }} - the basis consisting of all {{plural|Cartesian product|s}} of all open sets from {{M|\big((X_\alpha,\mathcal{J}_\alpha)\big)_{\alpha\in I} }}<ref group="Note">Badly phrased, it should mean all tuples of the form {{M|(U_\alpha)_{\alpha\in I} }} where {{M|1=\forall\alpha\in I[U_\alpha\in\mathcal{J}_\alpha]}}</ref>
{{Todo|Check this expression}}
==Notes==
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==References==
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