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ЖУРНАЛЫ // Математические заметки // Архив

Матем. заметки, 2025, том 118, выпуск 5, страницы 970–975 (Mi mzm14996)

Статьи, опубликованные в английской версии журнала

Two selection theorems for extremally disconnected spaces

V. Gutev

Bulgarian Academy of Sciences

Аннотация: The paper contains a very simple proof of Hasumi's classical theorem claiming 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.

Ключевые слова: set-valued mapping, upper semi-continuous, continuous selection, extremally disconnected space.

Поступило: 25.09.2024
После доработки: 07.08.2025
Принято к публикации: 22.08.2025

Язык публикации: английский


 Англоязычная версия: Mathematical Notes, 2025, 118:5, 970–975


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