The continuity of inverse in groups (Q2104405)

This article is a contribution to the question under which conditions a paratopological group is a topological group. For that the author introduces the concept of a \(\Delta\)-Baire space. A topological space \(X\) is a \(\Delta\)-Baire space if for every set \(P\subseteq X\times X\) containing the diagonal \(\Delta:=\{(x,x):x\in X\}\) and having the property that \(\{y\in X:(x,y)\in P\}\) is open for any \(x\in X\) there is an open nonempty set \(W\) with \(W\times W\subseteq \bar{P}\). A metrizable Baire space is an example for a \(\Delta\)-Baire space. It is proved that any \(\Delta\)-Baire paratopological group is a topological group. For several classes of topological spaces it is then shown that they are \(\Delta\)-Baire spaces.