Difference between revisions of "Product topology"
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Revision as of 19:21, 27 February 2015
Given a set X_{\alpha\in I} of indexed topological spaces, we define the product topology, denoted \prod_{\alpha\in I}X_\alpha (yes the Cartesian product) is the coarsest topology such that all the projection maps are continuous.
The projection maps are:
p_\alpha:\prod_{\beta\in I}X_\beta\rightarrow X_\alpha which take the tuple (x_\alpha)_{\alpha\in I}\rightarrow x_{\beta}
This leads to the main property of the product topology, which can best be expressed as a diagram. Will add that later.
TODO:
