Insertion of a measurable function

Kotzé, W. and Kubiak, T. (1994) Insertion of a measurable function. Journal of the Australian Mathematical Society, Series A, 57 (3). pp. 295-304. ISSN 1446-7887



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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.

Item Type:Article
Uncontrolled Keywords:real-valued function; σ-ring; measurable function; class α function; insertion; extension; separation; perfect space; normal; extremally disconnected; 54C50; 28A05; 28A20; 54C20; 54C45; 26A21; 54C30.
Subjects:Y Unknown > Subjects to be assigned
Divisions:Faculty > Faculty of Science > Mathematics (Pure & Applied)
ID Code:1421
Deposited On:29 Jul 2009
Last Modified:06 Jan 2012 16:20
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