According to the celebrated theorem of Comfort and Ross (1966), the product of an arbitrary family of pseudocompact topological groups is pseudocompact. We present an overview of several important generalizations of this result, both of “absolute” and “relative” nature. One of them is the preservation of functional boundedness for subsets of topological groups. Also we consider close notions of...

We define $\Delta$-Baire spaces. If a paratopological group $G$ is space, then topological group. Locally pseudocompact spaces, Baire $p$-spaces, $\Sigma$-spaces, products of \v{C}ech-complete spaces are

The article studies topological games that arise in the study of continuity operations groups with topology, such as paratopological and semitopological groups. These are modifications Banach--Mazur game. Given a two-player game $G(X)$ type, we define $\Gamma^G$-Baire, $\Gamma^G$-nonmeager $\Gamma^G$-spaces. A space $X$ is $\Gamma^G$-Baire if second player does not have winning strategy $G(X)$....

We discuss the class of paratopological groups which admits a transversal, T 1 -independent and -complementary group topology. show that Sorgenfrey line does not admit Hausdorff topology, gives negative answer to [5, Problem 10] . give very useful criterion for transversality in term submaximal prove if non-discrete topology G contains central subgroup transversal then so introduce concept PT -...