Category-theoretic fuzzy topological spaces and their dualities

Mustafa Demirci

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Category-theoretic fuzzy topological spaces and their dualities

机译：范畴理论的模糊拓扑空间及其对偶性

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摘要

It is shown in this paper that various approaches to fuzzy topological spaces can be extended to an abstract category C. In this respect, variety-based generalized topological spaces, variable-basis fuzzy topological spaces, fixed-basis fuzzy topological spaces and Hutton fuzzy topological spaces are defined in C. We also construct their respective categories, as well as establish a generalized Papert-Papert-Isbell style adjunction for each of them. These adjunctions are later on refined to equivalences, involving appropriate definitions of spatiality and sobriety.

机译：本文表明，可以将模糊拓扑空间的各种方法扩展到抽象类别C。在这方面，基于变体的广义拓扑空间，变基模糊拓扑空间，固定基模糊拓扑空间和Hutton模糊拓扑C中定义了空格。我们还构造了它们各自的类别，并为它们中的每一个建立了通用的Papert-Papert-Isbell风格附加语。后来将这些附加条件精炼为等效，包括对空间性和清醒性的适当定义。

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来源
《Fuzzy sets and systems》 |2013年第16期|1-24|共24页
作者
Mustafa Demirci;
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作者单位

Akdeniz University, Faculty of Sciences, Department of Mathematics, 07058 Antalya, Turkey;

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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
关键词
Category theory; Categorical topology; Adjoint situation; Duality; Lattice-valued topology; Many-valued topology; Fuzzy topology;

机译：范畴论;分类拓扑;伴随状况;二元性格值拓扑;多值拓扑;模糊拓扑;

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1. Stratified categorical fixed-basis fuzzy topological spaces and their duality [J] . Demirci Mustafa Fuzzy sets and systems . 2015,第maya15期

机译：分层分类固定基模糊拓扑空间及其对偶
2. A note on specialization L-preorder of L-topological spaces, L-fuzzifying topological spaces, and L-fuzzy topological spaces [J] . Wei Yao, Fu-Gui Shi Fuzzy sets and systems . 2008,第19期

机译：关于L-拓扑空间，L-模糊化拓扑空间和L-模糊拓扑空间的专业L阶的注记
3. Fuzzy topological entropy of fuzzy continuous functions on fuzzy topological spaces [J] . Uzzal Afsan B.M., Basu C.K. Applied mathematics letters . 2011,第12期

机译：模糊拓扑空间上模糊连续函数的模糊拓扑熵
4. Fuzzy semi-quantales, (L,M) quasi-fuzzy topological spaces and their duality [C] . Mustafa Demirci International Joint Conference on Computational Intelligence . 2015

机译：模糊半量子，（L，M）准模糊拓扑空间及其对偶
5. Topological and category-theoretic aspects of abstract elementary classes. [D] . Lieberman, Michael Joseph. 2009

机译：抽象基本类的拓扑和类别理论方面。
6. Weak forms of continuity in I-double gradation fuzzy topological spaces [O] . A Ghareeb -1

机译：I-双灰度模糊拓扑空间中的弱连续性形式
7. On Generalized Continuous Fuzzy Proper Function from a Fuzzy Topological Space to another Fuzzy Topological Space [O] . Al.Khafaje Et al. 2019

机译：关于从模糊拓扑空间到另一个模糊拓扑空间的广义连续模糊功效
8. Duality Beyond Sober Spaces: Topological Spaces and Observation Frames [R] . Bonsangue, M., Jacobs, B., Kok, J. N. 1994

机译：超越清醒空间的二元性：拓扑空间和观测框架

Category-theoretic fuzzy topological spaces and their dualities

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