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  • Insertion of a measurable function

  • Part of
  • Wesley Kotzé, Tomasz Kubiak
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 57 / Issue 3 / December 1994
    Published online by Cambridge University Press:
    09 April 2009, pp. 295-304
    Print publication:
    December 1994
    • Article
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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.