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Insertion of a measurable function
Published online by Cambridge University Press: 09 April 2009
Abstract
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.
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- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 57 , Issue 3 , December 1994 , pp. 295 - 304
- Copyright
- Copyright © Australian Mathematical Society 1994
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