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Abstract <p> 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. </p>

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Two Selection Theorems for Extremally Disconnected Spaces

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • V. Gutev

摘要

Abstract

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.