Restricted product

In mathematics, the restricted product is a construction in the theory of topological groups.

Let ${\displaystyle I}$ be an indexing set; ${\displaystyle S}$ a finite subset of ${\displaystyle I}$. If for each ${\displaystyle i\in I}$, ${\displaystyle G_{i}}$ is a locally compact group, and for each ${\displaystyle i\in I\backslash S}$, ${\displaystyle K_{i}\subset G_{i}}$ is an open compact subgroup, then the restricted product

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