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【期刊论文】On two weaker forms of continuous order-homomorphisms 1
李生刚, Sheng-Gang Li
Fuzzy Sets and Systems 101(1999)469-475,-0001,():
-1年11月30日
The aim of this paper is to find further connections between two different current researches on fuzzy topology: the one based on the concepts of neighborhood, filter and Zadeh function, and the other based on the concepts of remote neighborhood, ideal and order-homomorphism on fuzzy lattices. To approach this, the paper studies two weaker forms of continuous order-homomorphisms, the semi-continuous order-homomorphism and the weakly semi-continuous order-homomorphism between L-fuzzy topological spaces. These order-homomorphisms can be characterized in each of the notions: remote-neighborhood, neighborhood, ideal, filter and molecular net. In addition, some relations connecting weakly semi-continuous order-homomorphisms, semi-Hausdorff L-fts and Urysohn L-fts have also been established.
L-fuzzy topology, Semi-continuous order-homomorphism, Weakly semi-continuous order-homomorphism, Retraction
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【期刊论文】Weak topological categories 1
李生刚, Shenggang Li
Fuzzy Sets and Systems 93(1998)363-373,-0001,():
-1年11月30日
In order to provide a categorical framework for fuzzy topology, this paper proposes the concept of weak topological category, a weaker form of topological category. Properties of weak topological categories are investigated, and some examples of such category are provided. Moreover, the relationship between a useful weak topological category LTop, the category of L-fuzzy topological spaces and continuous L-valued Zadeh functions, and some of its subcategories is studied.
Fuzzy topology, Categorical topology, Fuzzy measurable space, Fuzzy uniform space
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【期刊论文】Separation axioms in L-fuzzy topological spaces (I): T0 and T1
李生刚, Sheng-Gang Li
Fuzzy Sets and Systems 116(2000)377-383,-0001,():
-1年11月30日
Using the notion of remote neighborhood, we dene the separation axioms T0 and T1 in L-fuzzy topological spaces (L-fts). The relations between our denitions, Hutton and Reilly's, and Wang's are discussed, and the separations of Hutton's fuzzy unit interval and Gantner's fuzzy real line are examined. Characterizations of these L-fts are proved and a series of properties of them are investigated. Moreover, some results on minimal T0 L-fts and T1 L-fts are established, which will be used immediately in our subsequent discussion.
Fuzzy topology, Axiom of separation, Remote neighborhood, Fuzzy unit interval, Fuzzy real line
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【期刊论文】Inverse limits in category LTop (I) 1
李生刚, Sheng-Gang Li
Fuzzy Sets and Systems 108(1999)235-241,-0001,():
-1年11月30日
This paper is devoted to the study of the inverse limits in LTop, the category of L-fuzzy topological spaces and continuous L-valued Zadeh-functions between them, where L is a completely distributive complete lattice. Structures of such limits are described and a series of their properties are investigated. Furthermore, the mappings between two arbitrary inverse systems is de ned and some of their properties are discussed for the case of category LTop.
Fuzzy topology, Category, Inverse system, Inverse limit, Mapping between inverse systems
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