The minimax equality \[ \inf_{t\in T}\sup_{x\in X}f(t,x) = \sup_{x\in X}\inf_{t\in T}f(t,x) \] is established in a non-standard case. Here \(T\) is a compact subinterval of the real line, but \(X\) is a compact metric space and the continuous function \(f\) is \(t\)-convex on \(T\) and satisfies a ``global maximum'' \(x\)-condition on \(X\). As an application a result of \textit{A. Asplund} and \textit{V. Pták} [Acta Math. 126, 53--62 (1971; Zbl 0203.44902)] is derived.