The congruence biframe as a quasi-uniform bicompletion
| Autor: | Graham R. Manuell |
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| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
010102 general mathematics General Topology (math.GN) Mathematics::General Topology Space (mathematics) 01 natural sciences 010101 applied mathematics Corollary If and only if Mathematics::Category Theory FOS: Mathematics Congruence (manifolds) Frame (artificial intelligence) Geometry and Topology Compactification (mathematics) 0101 mathematics Quotient Mathematics - General Topology 06D22 06B10 54E15 54E55 Mathematics |
| Zdroj: | Topology and its Applications. 273:106968 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2019.106968 |
| Popis: | K\"unzi and Ferrario have shown that a $T_0$ space is sober if and only if it is bicomplete in the well-monotone quasi-uniformity. We prove a pointfree version of this result: a strictly zero-dimensional biframe is a congruence biframe if and only if it is bicomplete in the same quasi-uniformity. As a corollary we obtain a new proof of a result of Plewe that a congruence frame is ultraparacompact. The main result makes use of a new construction of the bicompletion of a quasi-uniform biframe as a quotient of the Samuel compactification. Comment: 12 pages, 0 figures. To be published in Topology and its Applications |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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