On approximation of mappings with values in the space of continuous functions - Voloshyn, H.A.; Maslyuchenko, V.K.; Nesterenko, O.N. (Carpathian Mathematical Publications, 2012)
Using a theorem on the approximation of the identity in the Banach space C_u(Y) of all continuous functions g: Y→ R, defined on a metrizable compact Y with the uniform norm, we prove that for a topological space X, a metrizable compact Y, a linear subspace L of Y dense in C_u(Y) and a separately continuous function f: X× Y→ R there exists a sequence of jointly continuous functions f_n: X× Y→ R such that f_n^x = f(x, ·)L and f_n^x → f^x in C_u(Y) for each xX.