Two Selection Theorems for Extremally Disconnected Spaces
arXiv:2409.09490
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.