View source for Canonical projections of the product topology

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==Definition==
Let {{M|\big((X_\alpha,\mathcal{J}_\alpha)\big)_{\alpha\in I} }} be an arbitrary family of [[topological spaces]] and let {{M|(\prod_{\alpha\in I}X_\alpha,\mathcal{J})}} denote their product, considered with the [[product topology]], then, for each {{M|\beta\in I}} we get a [[map]]:
* {{M|\pi_\beta:\prod_{\alpha\in I}X_\alpha\rightarrow X_\beta}} given by: {{M|\pi_\beta:(x_\alpha)_{\alpha\in I}\mapsto x_\beta}}
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Sometimes denoted by {{M|p_\beta:\prod_{\alpha\in I}X_\alpha\rightarrow X_\beta}} instead. We'll use the two interchangeably but will always define them as a canonical projection.
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==See also==
* [[Canonical injection of the subspace topology]]
* [[Canonical injections of the disjoint union topology]]
==References==
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