Separately continuous weak selections on products

Extending results of García-Ferreira, Miyazaki, Nogura [4] and Gutev [9], we prove that: (i) if p is a non-isolated point of a space X and q a point of a space Y, then the existence of a separately continuous weak selection on the product space X×Y∖{(p,q)} implies that the pseudo-character of q in Y does not exceed the approaching number of p in X; (ii) if p is a non-isolated point of X and κ an uncountable regular cardinal such that the approaching number of p in X is less than κ, then the product space X×S does not admit a separately continuous weak selection for each stationary set S of κ with the order topology.