Report
Categorical Extension of Dualities: From Stone to de Vries and Beyond, I
| العنوان: | Categorical Extension of Dualities: From Stone to de Vries and Beyond, I |
|---|---|
| المؤلفون: | Dimov, G., Ivanova-Dimova, E., Tholen, W. |
| سنة النشر: | 2019 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - General Topology, 54D30, 54D15, 18A40, 18B30, 54E05, 54C10, 54G05, 06E15, 54H10, 03G05 |
| الوصف: | Propounding a general categorical framework for the extension of dualities, we present a new proof of the de Vries Duality Theorem for the category $\bf KHaus$ of compact Hausdorff spaces and their continuous maps, as an extension of a restricted Stone duality. Then, applying a dualization of the categorical framework to the de Vries duality, we give an alternative proof of the extension of the de Vries duality to the category $\bf Tych$ of Tychonoff spaces that was provided by Bezhanishvili, Morandi and Olberding. In the process of doing so, we obtain new duality theorems for both categories, $\bf{KHaus}$ and $\bf Tych$. Comment: 47 pages. This is a revised and expanded version of our paper arXiv:1906.06177v1 "Extensions of dualities and a new approach to the de Vries duality" |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1906.06177 |
| رقم الانضمام: | edsarx.1906.06177 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |