Dependence on \(\aleph\) coordinates of separately continuous functions of many variables and its analogs (Q6165355)

Let \(\aleph\) be an infinite cardinal and let \(X\) be the product of a family \((X_s\colon s\in S)\) of nontrivial completely regular spaces \(X_s\). It is known that every continuous function \(f\colon X\to\mathbb{R}\) depends on \(\aleph\) coordinates iff \(X\) is pseudo-\(\aleph^+\)-compact. Some necessary and sufficient conditions for the dependence on a certain number of coordinates of separately continuous functions of two or more variables on products were investigated in the last thirty years. In the present paper the author gives a new characterization for the (strongly) separately continuous function \(f\) defined on the product of nontrivial completely regular spaces to be dependent on \(\aleph\) coordinates (Theorem 5.5 and Corollary 5.6).