On continuity of $KC$-functions with values in Ceder plane

Abstract

We show that the Ceder plane $\mathbb{M}$ is a $\sigma$-metrizable space, which does not have a development. For every quasicontinuous mapping $f:X\to\mathbb{M}$ the continuity point set $C(f)$ is residual. We investigate the continuity point set $C(f)$ of a mapping $f:X\times Y\to \mathbb{M}$, which is quasicontinuous with respect to the first variable and continuous with respect to the second one.