Uniformities and covering properties for partial frames (I)
Publish Year: 1393
نوع سند: مقاله ژورنالی
زبان: English
View: 194
This Paper With 21 Page And PDF Format Ready To Download
- Certificate
- من نویسنده این مقاله هستم
استخراج به نرم افزارهای پژوهشی:
شناسه ملی سند علمی:
JR_CGASAT-2-1_001
تاریخ نمایه سازی: 23 شهریور 1400
Abstract:
Partial frames provide a rich context in which to do pointfree structured and unstructured topology. A small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. These axioms are sufficiently general to include as examples bounded distributive lattices, sigma-frames, kappa-frames and frames. Reflective subcategories of uniform and nearness spaces and lately coreflective subcategories of uniform and nearness frames have been a topic of considerable interest. In cite{jfas۹} an easily implementable criterion for establishing certain coreflections in nearness frames was presented. Although the primary application in that paper was in the setting of nearness frames, it was observed there that similar techniques apply in many categories; we establish here, in this more general setting of structured partial frames, a technique that unifies these. We make use of the notion of a partial frame, which is a meet-semilattice in which certain designated subsets are required to have joins, and finite meets distribute over these. After presenting our axiomatization of partial frames, which we call sels-frames, we add structure, in the form of sels-covers and nearness, and provide the promised method of constructing certain coreflections. We illustrate the method with the examples of uniform, strong and totally bounded nearness sels-frames. In Part (II) of this paper, we consider regularity, normality and compactness for partial frames.
Keywords:
frame , sels-frame , Z-frame , partial frame , sigma-frame , kappa-frame , meet-semilattice , nearness , Uniformity , strong inclusion , uniform map , coreflection , P-approximation , strong , totally bounded , regular , normal , compact
Authors
John Frith
Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag Rondebosch, ۷۷۰۱, South Africa.
Anneliese Schauerte
Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag Rondebosch, ۷۷۰۱, South Africa.
مراجع و منابع این Paper:
لیست زیر مراجع و منابع استفاده شده در این Paper را نمایش می دهد. این مراجع به صورت کاملا ماشینی و بر اساس هوش مصنوعی استخراج شده اند و لذا ممکن است دارای اشکالاتی باشند که به مرور زمان دقت استخراج این محتوا افزایش می یابد. مراجعی که مقالات مربوط به آنها در سیویلیکا نمایه شده و پیدا شده اند، به خود Paper لینک شده اند :