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  "body": "\n## Summary\n\nA topological monoid is a [[monoid|0N6R902FG1]] with a topology in which the multiplication is jointly continuous.\nIt is a [[topological semigroup|QXB6JDG68F]] that has an identity element.\nTopological monoids arise in algebraic topology, for example as Moore loop spaces, where loops of varying length are concatenated.\nThey also arise in the study of operator semigroups.\n\n## Explanations\n\n### L1 human\n\nA monoid is a set with an associative operation and a neutral element, like the natural numbers under addition with neutral element $0$.\nA topological monoid adds a topology so that the operation respects nearness.\nAn example is the set of real numbers under multiplication with the usual topology, with neutral element $1$.\nIt is not a group, since $0$ has no inverse, but it is a topological monoid.\n",
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