2024/09/14 by Valentin Gutev, Gutev, Valentin
Mathematics · #54C10 #54C20 #54C60 #54C65 #54D35 #54G05 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.2409.09490
openalex publication_date 2024/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.