极端断开空间的两个选择定理

arXiv - MATH - General Topology Pub Date : 2024-09-14 DOI:arxiv-2409.09490

Valentin Gutev

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引用次数: 0

摘要

这篇论文包含对经典的 Hasumi 定理的一个非常简单的证明，即定义在极端断开空间上的每个 usco 映射都有一个连续选择。论文还包含一个关于紧凑值连续映射的密集定义连续选择的最新结果的非常简单的证明，实际上是这个结果对所有有规则范围的uscomappings的推广。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Two Selection Theorems for Extremally Disconnected Spaces

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.

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arXiv - MATH - General Topology

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