J Austral Math Soc Ser A 57 pp295--304, 1994.

Insertion of a Measurable Function

Wesley Kotze and Tomasz Kubiak

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 Katetov-Tong insertion theorem, the Tietze extension theorem, Urysohn's lemma) are characterizations of normal s-rings. Likewise, similar theorems about extremely disconnectd spaces are true for s-rings of a certain type. This s-ring approach leads to general results on the existence of functions of class a.

1991 AMS Subject Classification: 54C50, 28A05, 28A20, 54C20, 54C45, 26A21, 54C30

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Authors

Wesley Kotze

Department of Mathematics, (Pure and Applied), Rhodes University, Grahamstown 6140, South Africa.

Tomasz Kubiak

Institute of Mathematics, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznan, Poland.