  Theorem 1 of [14], a minimax result for functions $f:X\times Y\to {\bf R}$,
where $Y$ is a real interval, was partially extended to the case where $Y$ is a
convex set in a Hausdorff topological vector space ([15], Theorem 3.2). In
doing that, a key tool was a partial extension of the same result to the case
where $Y$ is a convex set in ${\bf R}^n$ ([7], Theorem 4.2). In the present
paper, we first obtain a full extension of the result in [14] by means of a new
proof fully based on the use of the result itself via an inductive argument.
Then, we present an overview of the various and numerous applications of these
results.
