An enriched category approach to many valued topology

Dexue Zhang

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An enriched category approach to many valued topology

机译：一种丰富的类别方法，用于处理许多有价值的拓扑

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摘要

In this paper we discuss a basic question in fuzzy set theory: what is a many valued topology on a set X? An answer is presented by interpreting the axioms (two logical formulas) for classical topological spaces in the fuzzy setting making use of the intrinsic fuzzy partial order on the fuzzy power set of X. As preparation, a systematic investigation of fuzzy partial orders is presented from the viewpoint of enriched category theory.

机译：在本文中，我们讨论了模糊集理论中的一个基本问题：集合X上的多值拓扑是什么？通过使用X的模糊幂集上的固有模糊偏序来解释模糊集合中经典拓扑空间的公理（两个逻辑公式），从而给出答案。丰富范畴理论的观点。

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来源
《Fuzzy sets and systems》 |2007年第4期|p.349-366|共18页
作者
Dexue Zhang;
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作者单位

Department of Mathematics, Sichuan University, Chengdu 610064, China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类模糊数学;
关键词
commutative quantale; enriched category; enriched adjunction; yoneda embedding; complete Ω-lattice; fully ft-fuzzy topology; strong Ω-topology;

机译：可交换量子;丰富类别;丰富附加;超越嵌套;完全Ω格;完全模糊模糊拓扑;强Ω拓扑;

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2. Density in categorical topology via quantaloid-enriched categories [J] . Lai Hongliang, Shen Lili Topology and its applications . 2021,第Sepa1期

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3. Categories of lattice-valued closure (interior) operators and Alexandroff L-fuzzy topologies [J] . Ramadan A. A., Li L. Annals of the American Thoracic Society . 2019,第3期

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6. Low Dimensional Geometry and Topology Special Feature: Fukaya categories of the torus and Dehn surgery [O] . Yankı Lekili, Timothy Perutz 2011

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7. On Some Categories of L-valued sets and Many-valued Topologies: Theoretical Foundations [O] . Uļjane Ingrīda 2009

机译：关于L值集和多值拓扑的某些类别：理论基础

An enriched category approach to many valued topology

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