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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

Separate and Joint Properties of some Analogues of Pointwise Discontinuity