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A topological group is a group $G$ together with a topology on the elements of $G$ such that the group operation and group inverse function are both continuous (with respect to the topology).

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Density of irreducible matrix coefficients of a locally compact group

Let $G$ be a locally compact group and $I$ the set of matrix coefficient of irreducible unitary matrix coefficients of $G$. By Gelfand-Raikov's theorem and Stone-Weirestrass's theorem, for a compact $ …
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