Directed sets of topology: Tukey representation and rejection
In: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, Jg. 118 (2024-04-01), Heft 2
Online
serialPeriodical
Zugriff:
Every directed set is Tukey equivalent to (a) the family of all compact subsets, ordered by inclusion, of a (locally compact) space, to (b) a neighborhood filter, ordered by reverse inclusion, of a point (of a compact space, and of a topological group), and to (c) the universal uniformity, ordered by reverse inclusion, of a space. Two directed sets are Tukey equivalent if they are cofinally equivalent in the sense that they can both be order embedded cofinallyin a third directed set. In contrast, any totally bounded uniformity is Tukey equivalent to [κ]<ω, the collection of all finite subsets of κ, where κis the cofinality of the uniformity. All other Tukey types are ‘rejected’ by totally bounded uniformities. Equivalently, a compact space Xhas weight (minimal size of a base) equal to κif and only if the neighborhood filter of the diagonal is Tukey equivalent to [κ]<ω. A number of questions from the literature are answered with the aid of the above results.
Titel: |
Directed sets of topology: Tukey representation and rejection
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Autor/in / Beteiligte Person: | Feng, Ziqin ; Gartside, Paul |
Link: | |
Zeitschrift: | Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, Jg. 118 (2024-04-01), Heft 2 |
Veröffentlichung: | 2024 |
Medientyp: | serialPeriodical |
ISSN: | 1578-7303 (print) ; 1579-1505 (print) |
DOI: | 10.1007/s13398-023-01544-1 |
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