Topology/Product Spaces

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Let $\{(X_i, \tau_i)\}_{i\in I}$ be an indexed collection of topological spaces and let $X=\prod_{i\in I} X_i$ . For each $i\in I$ let $\pi_i:X\to X_i$ be the $i$ th coordinate projection. The product topology is the topology $τ$ on $X$ generated by sets of the form $\pi_i^{-1}[U_i]$ where $i\in I$ and $U_i\in\tau_i$ .

Topology/Product Spaces

From Wikibooks, the open-content textbooks collection

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