- Title
- Insertion of a measurable function
- Creator
- Kotzé, W
- Creator
- Kubiak, T
- Date Issued
- 1994
- Date
- 1994
- Type
- Article
- Identifier
- vital:6785
- Identifier
- http://hdl.handle.net/10962/d1006928
- Description
- 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.
- Format
- 10 pages
- Format
- Publisher
- Journal of the Australian Mathematical Society
- Language
- English
- Relation
- Kotzé, W. and Kubiak, T. (1994) Insertion of a measurable function. Journal of the Australian Mathematical Society, Series A, 57 (3). pp. 295-304. Available at: http://dx.doi.org/10.1017/S1446788700037708
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