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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.

Keywords

Cite

@article{arxiv.2409.09490,
  title  = {Two Selection Theorems for Extremally Disconnected Spaces},
  author = {Valentin Gutev},
  journal= {arXiv preprint arXiv:2409.09490},
  year   = {2025}
}
R2 v1 2026-06-28T18:44:48.816Z