What is it about?
In General Topology, there is a close paralellism between the theories of convergence of nets and of filters, in which "subnet" corresponds to "finer filter", but this relationship depends on the notion of subnet that one uses. Various authors have defined, for fuzzy topological spaces, the convergence of fuzzy filters and fuzzy nets, and have obtained connections between these theories; however these authors do not obtain a satisfactory relation between a fuzzy net and the fuzzy net based on the prefilter generated by it.
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Why is it important?
In General Topology, there is a close paralellism between the theories of convergence of nets and of filters, in which "subnet" corresponds to "finer filter", but this relationship depends on the notion of subnet that one uses. Various authors have defined, for fuzzy topological spaces, the convergence of fuzzy filters and fuzzy nets, and have obtained connections between these theories; however these authors do not obtain a satisfactory relation between a fuzzy net and the fuzzy net based on the prefilter generated by it. In this paper we define for fuzzy nets a new notion of fuzzy subnet, that solves this question.
Perspectives
In General Topology, there is a close paralellism between the theories of convergence of nets and of filters, in which "subnet" corresponds to "finer filter", but this relationship depends on the notion of subnet that one uses. Various authors have defined, for fuzzy topological spaces, the convergence of fuzzy filters and fuzzy nets, and have obtained connections between these theories; however these authors do not obtain a satisfactory relation between a fuzzy net and the fuzzy net based on the prefilter generated by it. In this paper we define for fuzzy nets a new notion of fuzzy subnet, that solves this question.
Francisco Gallego Lupianez
University Complutense
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This page is a summary of: On fuzzy subnets, Fuzzy Sets and Systems, May 2001, Elsevier,
DOI: 10.1016/s0165-0114(99)00085-8.
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