Insertion of a measurable function

Journal of the Australian Mathematical Society

Wesley Kotzé¹ 

[1] Tomasz Kubiak

关键词: 54C50;    28A05;    28A20;    54C20;    54C45;    26A21;    54C30;   

DOI  :  10.1017/S1446788700037708

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Some theorems on the existence of continuous real-valued functions on a topological space (for example, insertion, extension, and separation theorems) can be proved without involving uncountable unions of open sets. In particular, it is shown that well-known characterizations of normality (for example the Katětov-Tong insertion theorem, the Tietze extension theorem, Urysohn's lemma) are characterizations of normal σ-rings. Likewise, similar theorems about extremally disconnected spaces are true for σ-rings of a certain type. This σ-ring approach leads to general results on the existence of functions of class α.

【 授权许可】

Unknown