The fuzzy Hausdorff-Bourbaki structures and their relations with the fuzzy Vietoris structures (Q1826155)
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scientific article; zbMATH DE number 4122805
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The fuzzy Hausdorff-Bourbaki structures and their relations with the fuzzy Vietoris structures |
scientific article; zbMATH DE number 4122805 |
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The fuzzy Hausdorff-Bourbaki structures and their relations with the fuzzy Vietoris structures (English)
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1989
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The Hausdorff-Bourbaki fuzzy uniformity [\textit{R. Lowen}, Fuzzy Sets Syst. 9, 278-311 (1983; Zbl 0546.54010)] is shown to be the supremum of the upper and lower fuzzy quasi-uniformities. The relations of these structures with the semi-Vietoris fuzzy neighborhood structures are studied. For example, on the Weiss precompact fuzzy sets the Vietoris fuzzy neighborhood system is finer than that derived from the Hausdorff- Bourbaki structure with equality holding on the Weiss-compact fuzzy sets.
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fuzzy uniform space
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fuzzy neighborhood space
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Hausdorff-Bourbaki fuzzy uniformity
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semi-Vietoris fuzzy neighborhood structures
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Weiss precompact fuzzy sets
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Weiss-compact fuzzy sets
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