On approximation of the separately and jointly continuous functions - Voloshyn, H.A.; Maslyuchenko, V.K.; Maslyuchenko, O.V. (Carpathian Mathematical Publications, 2010)
We investigate the following problem: which dense subspaces L of the Banach space C(Y) of continuous functions on a compact Y and topological spaces X have such property, that for every separately or jointly continuous functions f: X× Y → R there exists a sequence of separately or jointly continuous functions f_n: X× Y → R such, that f_n^x=f_n(x, ·) L for arbitrary nN, xX and f_n^x ightrightarrows f^x on Y for every xX? In particular, it was shown, if the space C(Y) has a basis that every jointly continuous function f: X× Y → R has jointly continuous approximations f_n such type.