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A semigroup $X$ endowed with a topology is called $\bullet$ a topological semigroup if the semigroup operation $X\times X\to X$ is continuous; $\bullet$ a semitopological semigroup if for every $a,b\...

In a topological group, for any neighborhood $U$ of the origin, there is another such neighborhood with the property that $V.V\subseteq U.$ I conjecture a similar property for topological inverse ...