Equi-Cliquishness and The Hahn Property

We study the joint continuity of mappings of two variables. In particular, we show that for a Baire space X, a second countable space Y and a metric space Z, a map f : X × Y → Z has the Hahn property (i.e., there is a residual subset A of X such that A × Y ⊆ C(f)) if and only if f is locally equi-cliquish with respect to y and {x ∈ X: f^x is continuous} is a residual subset of X.