Frobenius identities and geometrical aspects of Joyal-Tierney Theorem

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-10-31 DOI:10.1016/j.topol.2024.109127

Jorge Picado , Aleš Pultr

引用次数: 0

Abstract

Open and related maps in the point-free context are studied from a consequently geometric perspective: that is, the opens are concrete well-defined subsets, images of localic maps are set-theoretic images

f [U]

, etc. We present a short proof of Joyal-Tierney Theorem in this setting, a (geometric) characteristic of localic maps that are just complete, and prove that open localic maps also preserve a natural type of sublocales more general than the open ones. A crucial role is played by Frobenius identities that are briefly discussed also in their general aspects.

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弗罗贝纽斯等式和乔亚尔-蒂尔尼定理的几何方面

无点背景下的开立映射和相关映射主要是从几何的角度来研究的：也就是说，开立映射是具体的定义明确的子集，局部映射的图像是集合论图像 f[U] 等。我们简短地证明了这种情况下的乔亚-蒂尔尼定理（Joyal-Tierney Theorem），这是局部映射的一个（几何）特征，即局部映射是完全的，并证明了开放局部映射也保留了一种比开放映射更一般的自然子域。弗罗贝纽斯等式起着至关重要的作用，我们也将简要讨论它们的一般方面。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.