Strongly separately continuous and separately quasicontinuous functions \(f\, :\, l^2\, \to \, \mathbb{R}\) (Q2510978)

The author provides a sufficient condition for a strongly separately continuous function \(f: l^2\to \mathbb{R}\) at a point to be continuous at that point. Then he introduces the notion of a separately quasicontinuous function \(f: l^2\to \mathbb{R}\) and provides a sufficient condition for a separately quasicontinuous function on \(l^2\) to be quasicontinuous. Finally, it exhibits a class of determining sets for the class of separately continuous functions on \(l^2\). Recall that a subset \(M\) of a set \(X\) is said to be a determining set for a class \(\mathcal F\) of functions defined on \(X\) if for any couple of functions \(f, g \in \mathcal{F}\) the equality \(f(x) = g(x)\) for every \(x \in M\) implies \(f(x) = g(x)\) for every \(x \in X\).