When is a category of adherence-determined convergences simple?

When is a category of adherence-determined convergences simple?

We provide a characterization of classes of filters D for which the full subcategory fixAD of Conv formed by convergences determined by the adherence of filters of the class D is simple in Conv. Along the way, we also elucidate when two classes of filters result in the same category of adherence-det...

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Veröffentlicht in:Topology and its applications 2022-12, Vol.322, p.108319, Article 108319
Hauptverfasser: Mynard, Frédéric, Wojciechowski, Jerzy
Format: Artikel
Sprache:eng
Schlagworte:
Adherence-determined convergence
Convergence space
Hypotopology
Paratopology
Pseudotopology
Simple category
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Zusammenfassung:We provide a characterization of classes of filters D for which the full subcategory fixAD of Conv formed by convergences determined by the adherence of filters of the class D is simple in Conv. Along the way, we also elucidate when two classes of filters result in the same category of adherence-determined convergences. As an application of the main result, we show that the category of hypotopologies is not simple, thus answering a question from [24].
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2022.108319