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Separate and joint continuity in Baire groups. (English) Zbl 0938.22001

A group \(G\) is called semitopological (resp. paratopological) if \(G\) is equipped with a topology in which the multiplication is separately (resp. jointly) continuous. The main result of the article claims that every Baire, Moore semitopological group is paratopological. To prove this the author introduces the notion of JC-type space. A topological space \(X\) is a JC-type space if, for every separately continuous function \(f: X \times X \to X\), the set of points of continuity of \(f\) is nonempty. Then he proves that every first countable JC-type semitopological group is paratopological. Since every Baire, Moore space is of JC-type, the main theorem follows.

MSC:

22A20 Analysis on topological semigroups
54E18 \(p\)-spaces, \(M\)-spaces, \(\sigma\)-spaces, etc.
54H15 Transformation groups and semigroups (topological aspects)
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