MATHEMATICS

Some properties of the set of maps in the pointwise topology

A. A. Fedorov

Tomsk State University, Tomsk, Russian Federation

Abstract: 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 $P$.

Keywords: topology of pointwise convergence, net weight, topological spaces of mappings.

UDC: 515.127

Received: 21.11.2014