Two Selection Theorems for Extremally Disconnected Spaces
General Topology
2025-08-08 v2
Abstract
The paper contains a very simple proof of the classical Hasumi's theorem that each usco mapping defined on an extremally disconnected space has a continuous selection. The paper also contains a very simple proof of a recent result about extension of densely defined continuous selections for compact-valued continuous mappings, in fact a generalisation of this result to all usco mappings with a regular range.
Cite
@article{arxiv.2409.09490,
title = {Two Selection Theorems for Extremally Disconnected Spaces},
author = {Valentin Gutev},
journal= {arXiv preprint arXiv:2409.09490},
year = {2025}
}