Topology on BL-algebras

In this paper, by using a special family of filters on a BL-algebra L, we construct a topology τ on L, show that (L,τ) is a topological BL-algebra, find the closure of any subsets of L and obtain some conditions under which that (L,τ) is a Hausdorff space. Also, we prove some theorems about connecte...

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Bibliographic Details
Published inFuzzy sets and systems Vol. 289; pp. 137 - 150
Main Authors Zahiri, O., Borzooei, R.A.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.04.2016
Subjects
Cauchy sequence
Closures
Completion
Connected component
Construction
Fuzzy logic
Fuzzy set theory
Limit
Quotients
Theorems
Topological BL-algebra
Topology
Fuzzy logic
Completion
Topological BL-algebra
Limit
Cauchy sequence
Connected component
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Summary:In this paper, by using a special family of filters on a BL-algebra L, we construct a topology τ on L, show that (L,τ) is a topological BL-algebra, find the closure of any subsets of L and obtain some conditions under which that (L,τ) is a Hausdorff space. Also, we prove some theorems about connected components of this topological space and use them to construct a quotient semitopological BL-algebras. Finally, we introduce the concept of complete BL-algebra and attempt to construct a complete BL-algebra from L.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2014.11.014