  We solve a problem on a construction of a separately continuous mapping with
the given diagonal, which is the pointwise limit of a sequence of continuous
mappings valued in an equiconnected space. We construct an example of a
closed-valued separately continuous mapping $f:[0,1]^2\to \mathbb R$ with an
everywhere discontinuous diagonal. The example shows that the results on the
joint continuity point set of compact-valued separately continuous mappings can
not be generalized to the case of closed-valued mappings.
