تقرير
Pervin spaces and Frith frames: bitopological aspects and completion
| العنوان: | Pervin spaces and Frith frames: bitopological aspects and completion |
|---|---|
| المؤلفون: | Borlido, Célia, Suarez, Anna Laura |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - General Topology, 06D22, 54E55, 06D50 |
| الوصف: | A Pervin space is a set equipped with a bounded sublattice of its powerset, while its pointfree version, called Frith frame, consists of a frame equipped with a generating bounded sublattice. It is known that the dual adjunction between topological spaces and frames extends to a dual adjunction between Pervin spaces and Frith frames, and that the latter may be seen as representatives of certain quasi-uniform structures. As such, they have an underlying bitopological structure and inherit a natural notion of completion. In this paper we start by exploring the bitopological nature of Pervin spaces and of Frith frames, proving some categorical equivalences involving zero-dimensional structures. We then provide a conceptual proof of a duality between the categories of $T_0$ complete Pervin spaces and of complete Frith frames. This enables us to interpret several Stone-type dualities as a restriction of the dual adjunction between Pervin spaces and Frith frames along full subcategory embeddings. Finally, we provide analogues of Banaschewski and Pultr's characterizations of sober and $T_D$ topological spaces in the setting of Pervin spaces and of Frith frames, highlighting the parallelism between the two notions. Comment: 25 pages |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2303.00443Test |
| رقم الانضمام: | edsarx.2303.00443 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |