Some properties of the set of maps in the pointwise topology

This paper discusses topological properties of spaces of mappings (not necessarily continuous) in the pointwise topology. In particular, it is proved that $|T_1|\leqslant nw(P)\leqslant |T|$, where $P$ is a subset of real functions of a real variable having an at most countable sets of points of discontinuity, $T$ is the union of all sets of discontinuities of functions from $P$, and $T_1$ is the union of all sets of first kind discontinuities of functions from $P$.