English

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 f:[0,1]2Rf:[0,1]^2\to \mathbb R 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.

Keywords

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}
}
R2 v1 2026-06-22T12:41:43.725Z