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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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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Abstract 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.
AbstractList 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.
In this paper, by using a special family of filters on a BL-algebra L, we construct a topology tau on L, show that is a topological BL-algebra, find the closure of any subsets of L and obtain some conditions under which that 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.
Author Zahiri, O.
Borzooei, R.A.
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Cites_doi 10.1007/s00500-012-0852-2
10.1002/malq.200610035
10.1007/s00153-003-0178-y
10.1016/S0165-0114(01)00098-7
10.4134/CKMS.2004.19.2.219
10.1023/A:1022935811257
10.1007/s00500-012-0808-6
10.1007/s001530100088
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Keywords Fuzzy logic
Completion
Topological BL-algebra
Limit
Cauchy sequence
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Snippet 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...
In this paper, by using a special family of filters on a BL-algebra L, we construct a topology tau on L, show that is a topological BL-algebra, find the...
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SubjectTerms Cauchy sequence
Closures
Completion
Connected component
Construction
Fuzzy logic
Fuzzy set theory
Limit
Quotients
Theorems
Topological BL-algebra
Topology
Title Topology on BL-algebras
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