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Topological semigroups/monoids: topological space endowed with a continuous semigroup/monoid structure, or, equivalently, semigroup/monoid endowed with a compatible topology.

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Making the powerset into a topological monoid

Every monoid $X$ induces a monoid structure $\circledast$ on $\mathcal{P}(X)$ via $$U\circledast V := \{uv\ |\ u\in U,v\in V\}.$$ Moreover, a morphism of monoids $f\colon X\to Y$ induces a morphism of …
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