A solution of a problem by M. Henriksen and R.G. Woods. (Q1412701)

An example of a complete metric space is given with the following properties: \textbf{(1) }Every separately continuous real function defined on the product \(X\times X\) has a dense set of points of continuity; \textbf{(2) }There exists a separately continuous real function defined on \(X\times X\) for which the set of continuity points contains no non-empty set of the form \(A\times X\) or \(X\times B\).