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$m$-topological group; semitopological group; paratopological group; topological group; topology of pointwise convergence; Eberlein compact; weak functional tightness
In this paper, we show that it is possible to extend the Ellis theorem, establishing the relations between axioms of a topological group on a new class $\mathcal N$ of spaces containing all countably compact spaces in the case of Abelian group structure. We extend statements of the Ellis theorem concerning separate and joint continuity of group inverse on the class of spaces $\mathcal N$ that gives some new examples and statements for the $C_p$-theory and theory of topologically homogeneous spaces.
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