{
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  "slug": "compactly-generated-group",
  "title": "Compactly generated group",
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  "lead": "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.",
  "body": "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. ==References==",
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    "title": "Compactly generated group",
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      {
        "family": "Anticloud FZ LLE",
        "literal": "Anticloud FZ LLE"
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    ],
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    "publisher": "Anticloud FZ LLE",
    "publisher-place": "Dubai, United Arab Emirates",
    "URL": "https://encyclopegia.org/a/compactly-generated-group",
    "issued": {
      "date-parts": [
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          2026,
          11,
          15
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