Insertion of a measurable function
- Authors: Kotzé, W , Kubiak, T
- Date: 1994
- Language: English
- Type: Article
- Identifier: vital:6785 , 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.
- Full Text:
- Date Issued: 1994
- Authors: Kotzé, W , Kubiak, T
- Date: 1994
- Language: English
- Type: Article
- Identifier: vital:6785 , 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.
- Full Text:
- Date Issued: 1994
A class of ideals of the centre of a group ring
- Authors: O'Reilly, M F
- Date: 1981
- Language: English
- Type: Article
- Identifier: vital:6786 , http://hdl.handle.net/10962/d1006929
- Description: Reynolds (1972), using character-theory, showed that the p-section sums span an ideal of the centre Z(kG) of the group algebra of a finite group G over a field k of characteristic dividing the order of G. In O'Reilly (1973) a character-free proof was given. Here we extend these techniques to show the existence of a wider class of ideals of Z(kG).
- Full Text:
- Date Issued: 1981
- Authors: O'Reilly, M F
- Date: 1981
- Language: English
- Type: Article
- Identifier: vital:6786 , http://hdl.handle.net/10962/d1006929
- Description: Reynolds (1972), using character-theory, showed that the p-section sums span an ideal of the centre Z(kG) of the group algebra of a finite group G over a field k of characteristic dividing the order of G. In O'Reilly (1973) a character-free proof was given. Here we extend these techniques to show the existence of a wider class of ideals of Z(kG).
- Full Text:
- Date Issued: 1981
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