Compactly generated group
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In mathematics, a compactly generated (topological) group is a topological group G which is algebraically generated by one of its compact subsets. This should not be confused with the unrelated notion (widely used in algebraic topology) of a compactly generated space -- one whose topology is generated (in a suitable sense) by its compact subspaces.
In mathematics, a compactly generated (topological) group is a topological group G which is algebraically generated by one of its compact subsets. This should not be confused with the unrelated notion (widely used in algebraic topology) of a compactly generated space -- one whose topology is generated (in a suitable sense) by its compact subspaces. \langle K\rangle = \bigcup_{n \in \mathbb{N}} (K \cup K^{-1})^n = G. So if K is symmetric, i.e. K = K −1 , then G = \bigcup_{n \in \mathbb{N}} K^n.
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