View source for Product topology

Given a set {{M|X_{\alpha\in I} }} of [[Indexing set|indexed]] [[Topological space|topological spaces]], we define the product topology, denoted <math>\prod_{\alpha\in I}X_\alpha</math> (yes the [[Cartesian product]]) is the coarsest topology such that all the [[Projection map|projection maps]] are continuous.

The projection maps are:

<math>p_\alpha:\prod_{\beta\in I}X_\beta\rightarrow X_\alpha</math> which take the [[Tuple|tuple]] <math>(x_\alpha)_{\alpha\in I}\rightarrow x_{\beta}</math>

This leads to the main property of the product topology, which can best be expressed as a diagram. Will add that later.
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{{Definition|Topology}}