Lowen LM-fuzzy topological spaces

Authors:
Hai-Yang Li;Ji-Gen Peng
Affiliations:
Department of Mathematics, Xi'an Jiaotong University, Xi'an 710049, PR China and School of Science, Xi'an Polytechnic University, Xi'an 710048, PR China;Department of Mathematics, Xi'an Jiaotong University, Xi'an 710049, PR China and Department of Mathematics, Xi'an Jiaotong University, Xi'an 710049, PR China
Venue:
Fuzzy Sets and Systems
Year:
2012

Citing 7
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Abstract and concrete categories

Abstract and concrete categories
The categorical topology approach to fuzzy topology and fuzzy convergence

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Categories isomorphic to FNS

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L-Fuzzifying topologies as L-topologies

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(IC) L-cotopological spaces

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Lattice-valued induced fuzzy topological spaces

Fuzzy Sets and Systems

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Abstract

The aim of this paper is to define and study Lowen LM-fuzzy topological spaces. We discuss the basic properties of Lowen LM-fuzzy topological spaces, and introduce the notions of interior Lowen topology and exterior Lowen topology of an LM-fuzzy topology and prove that LLM-FTop (the category of Lowen LM-fuzzy topological spaces) is isomorphism-closed and simultaneously bireflective and bicoreflective in SLM-FTop (the category of stratified LM-fuzzy topological spaces). Moreover, we also prove that an LM-fuzzy topological space is an induced LM-fuzzy topological space iff it is a Lowen LM-fuzzy topological space and an (IC)LM-fuzzy topological space.