Metrizability on (semi)topological BL-algebras

Borzooei, Rajab Ali; Rezaei, Gholam Reza; Kouhestani, Nader

doi:10.1007/s00500-012-0852-2

Cited by 21 publications

(12 citation statements)

References 7 publications

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“…Proposition 2.12 (Borzooei et al 2012) Let F be a filter in a BL-algebra A which satisfies maximum condition. Then for any x; y 2 A Separation axioms in (semi)topological quotient BL-algebras 1221…”

Section: Preliminarymentioning

confidence: 98%

“…Definition 2.11 (Borzooei et al 2012) Let A be a BLalgebra. We call a filter F satisfies maximum condition if for each x 2 A; x F has a maximum.…”

Section: Preliminarymentioning

confidence: 99%

“…Also Arhangel'skii (2008) introduce prenorm on groups and study continuous prenorms on topological groups. Borzooei et al (2011) defined semitopological and topological BL-algebras, and they stated and proved some theorems that determine the relationships between them. They studied relations between T i spaces and BL-algebras endowed with a topology.…”

Section: Introductionmentioning

confidence: 99%

“…They prove that in a regular topological BL-algebra, T 1 topological BL-algebra is equivalent to Hausdorff topological BL-algebra. In Borzooei et al (2012), they introduced quasi-filter neighborhoods and studied metrizability on (semi)topological BL-algebras. In this paper, in Sect.…”

Section: Introductionmentioning

confidence: 99%

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Separation axioms in (semi)topological quotient BL-algebras

2012

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Section: Preliminarymentioning

confidence: 98%

“…Definition 2.11 (Borzooei et al 2012) Let A be a BLalgebra. We call a filter F satisfies maximum condition if for each x 2 A; x F has a maximum.…”

Section: Preliminarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Separation axioms in (semi)topological quotient BL-algebras

2012

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“…For example Di Nola and Leustean [11] studied compact representations of BL-algebras, Ciungu [8] investigated some concepts of convergence in the class of perfect BL-algebras, Mi Ko and Kim [17] studied relationships between closure operators and BL-algebras, Haveshki et al [14] applied filters to construct a topology on BL-algebras. Borzooei et al [4] defined semitopological and topological BL-algebras, and they stated and proved some theorems that determine the relationships between them. In [5], Borzooei et al introduced quasi-filter neighborhoods and studied metrizability on (semi)topological BL-algebras.…”

Section: Introductionmentioning

confidence: 99%

Semitopological BL-Algebras and MV -Algebras

Zahiri¹,

Borzooei²

2014

Demonstratio Mathematica

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Abstract. In this paper, by considering the notion of upsets, for any element x of a BL-algebra L, we construct a topology τx on L and show that L-algebras with this topology formes a semitopological BL-algebras. Then we obtain some of the topological aspects of this structure such as connectivity and compactness. Moreover, we introduced two kinds of semitopological M V -algebra by using two kinds of definition of M V -algebra and show that they are equivalent. IntroductionIn [13], Hájek proposed his logic BL as a common fragment of all traditional many valued logics (Łukasiewicz, Gödel and Product Logics). In [16], BL has been proved to be complete with respect to a variety of algebras called BL-algebras. BL-algebras are the algebraic structure for Hájek's Basic Logic. M V -algebras, Gödel algebras and Product algebras are the most known classes of BL-algebras. In the last 10 years, many mathematicians have studied the properties of BL-algebras endowed with a topology. 2010 Mathematics Subject Classification: 03G25, 54E15, 54H99.

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