When the maximum ring of quotients of \(C(X)\) is uniformly complete (Q5948942)
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scientific article; zbMATH DE number 1672467
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | When the maximum ring of quotients of \(C(X)\) is uniformly complete |
scientific article; zbMATH DE number 1672467 |
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When the maximum ring of quotients of \(C(X)\) is uniformly complete (English)
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12 November 2001
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uniform quotients spaces
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uniformly complete
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The article is devoted to an investigation of so-called uniform quotients spaces, which are Tychonoff spaces \(X\) such that the maximum ring of quotients of \(C(X)\) is uniformly complete.NEWLINENEWLINENEWLINECharacterizations of uniform quotients spaces in terms of Dedekind-MacNeille completeness, lateral completeness or spaces of dense constancies are studied in several theorems and corollaries. In particular, the following is proved: Theorem 3.9. Suppose \(X\) is a compact metric space. Then \(X\) is a uniform quotients space if and only if there is a dense subset of isolated points.
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