Topology on BL-algebras

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 in:Fuzzy sets and systems Vol. 289; pp. 137 - 150
Main Authors: Zahiri, O., Borzooei, R.A.
Format: Journal Article
Language:English
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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Description
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