Separate and Joint Properties of some Analogues of Pointwise Discontinuity

We study separate and joint properties of pointwise discontinuity, simple continuity and mild continuity of functions of two variables. In particular, it is shown that for a Baire space X, aBaire space Y which has a countable pseudobase and for a metric space Z, a function ƒ : X×Y → Z is pointwise discontinuous if and only if f satisfies (α, β)-condition and condition (C), and M = {x ∊ X : C(ƒ^x) = Y } is a residual subset of X. In addition, a characterization of simple continuity for mappings of one and two variables is given