Functorial Quasi-Uniformities on Frames
نویسندگان
چکیده
In this paper we present a unified study of functorial frame quasiuniformities by means of Weil entourages and frame congruences. In particular, we use the pointfree version of the Fletcher construction, introduced by the authors in a previous paper, to describe all functorial transitive quasi-uniformities.
منابع مشابه
Totally bounded frame quasi-uniformities
This paper considers totally bounded quasi-uniformities and quasi-proximities for frames and shows that for a given quasi-proximity ⊳ on a frame L there is a totally bounded quasi-uniformity on L that is the coarsest quasi-uniformity, and the only totally bounded quasi-uniformity, that determines ⊳. The constructions due to B. Banaschewski and A. Pultr of the Cauchy spectrum ψL and the compacti...
متن کاملAnother proof of Banaschewski's surjection theorem
We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...
متن کاملAsymmetric filter convergence and completeness
Completeness for metric spaces is traditionally presented in terms of convergence of Cauchy sequences, and for uniform spaces in terms of Cauchy filters. Somewhat more abstractly, a uniform space is complete if and only if it is closed in every uniform space in which it is embedded, and so isomorphic to any space in which it is densely embedded. This is the approach to completeness used in the ...
متن کاملA NOTE ON THE RELATIONSHIP BETWEEN HUTTON'S QUASI-UNIFORMITIES AND SHI'S QUASI-UNIFORMITIES
This note studies the relationship between Hutton's quasi-uniformities and Shi's quasi-uniformities. It is shown that when $L$ satisfies``multiple choice principle" for co-prime elements, the category of Hutton's quasi-uniform spaces is a bireflective full subcategory of the category of Shi's quasi-uniform spaces. Especially, if the remote-neighborhood mapping defined by Shi preserves arbitrary...
متن کاملAn Introduction to the Theory of Quasi-uniform Spaces
If the symmetry condition in the definition of a pseudometric is deleted, the notion of a quasi-pseudometric is obtained. Asymmetric distance functions already occur in the work of Hausdorff in the beginning of the twentieth century when in his book on set-theory [27] he discusses what is now called the Hausdorff metric of a metric space. A family of pseudo-metrics on a set generates a uniformi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Applied Categorical Structures
دوره 13 شماره
صفحات -
تاریخ انتشار 2005