Diagonals of separately continuous multi-valued mappings
General Topology
2016-02-03 v1
Abstract
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 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.
Cite
@article{arxiv.1602.00845,
title = {Diagonals of separately continuous multi-valued mappings},
author = {O. Fotiy and V. Mykhaylyuk and O. Sobchuk},
journal= {arXiv preprint arXiv:1602.00845},
year = {2016}
}