Some properties of the set of maps in the pointwise topology
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 6 (2014), pp. 55-58
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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.
@article{VTGU_2014_6_a5,
author = {A. A. Fedorov},
title = {Some properties of the set of maps in the pointwise topology},
journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
pages = {55--58},
year = {2014},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VTGU_2014_6_a5/}
}
A. A. Fedorov. Some properties of the set of maps in the pointwise topology. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 6 (2014), pp. 55-58. http://geodesic.mathdoc.fr/item/VTGU_2014_6_a5/
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