Box topology

Stub grade: B

This page is a stub

This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:

Not that important because we have the product topology page, however it should be a slightly bigger stub page!

Definition

Let [ilmath]\big((X_\alpha,\mathcal{J}_\alpha)\big)_{\alpha\in I} [/ilmath] be an arbitrary family of topological spaces. The box topology is the topology generated by the following basis:

• [ilmath]\mathcal{B}:=\{\prod_{\alpha\in I}U_\alpha\ \vert\ (U_\alpha)_{\alpha\in I}\in\prod_{\alpha\in I}\mathcal{J}_\alpha\}[/ilmath] - the basis consisting of all Cartesian products of all open sets from [ilmath]\big((X_\alpha,\mathcal{J}_\alpha)\big)_{\alpha\in I} [/ilmath]

---

TODO: Check this expression

---