Interval topology of lattice effect algebras

Qiang Lei; Junde Wu; Ronglu Li

doi:10.1016/j.aml.2009.01.008

Interval topology of lattice effect algebras

Qiang Lei^*
, Junde Wu
, Ronglu Li

^*Corresponding author for this work

School of Mathematics

Zhejiang University
Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

Let (E, ⊥, ⊕, 0, 1) be a lattice effect algebra and τ_i its interval topology. In this work we show that if the operation ⊕ is continuous with respect to τ_i, then τ_i is Hausdorff. In addition, we also show that if (E, ⊥, ⊕, 0, 1) is a complete M V-effect algebra and τ_i is a Hausdorff topology, then the operations ⊕, ⊖, ∨ and ∧ are τ_i continuous.

Original language	English
Pages (from-to)	1003-1006
Number of pages	4
Journal	Applied Mathematics Letters
Volume	22
Issue number	7
DOIs	https://doi.org/10.1016/j.aml.2009.01.008
State	Published - Jul 2009

Keywords

Atom
Continuity of operations
Interval topology
Lattice effect algebra
M V-effect algebra

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10.1016/j.aml.2009.01.008

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title = "Interval topology of lattice effect algebras",

abstract = "Let (E, ⊥, ⊕, 0, 1) be a lattice effect algebra and τi its interval topology. In this work we show that if the operation ⊕ is continuous with respect to τi, then τi is Hausdorff. In addition, we also show that if (E, ⊥, ⊕, 0, 1) is a complete M V-effect algebra and τi is a Hausdorff topology, then the operations ⊕, ⊖, ∨ and ∧ are τi continuous.",

keywords = "Atom, Continuity of operations, Interval topology, Lattice effect algebra, M V-effect algebra",

author = "Qiang Lei and Junde Wu and Ronglu Li",

year = "2009",

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doi = "10.1016/j.aml.2009.01.008",

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volume = "22",

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T1 - Interval topology of lattice effect algebras

AU - Lei, Qiang

AU - Wu, Junde

AU - Li, Ronglu

PY - 2009/7

Y1 - 2009/7

N2 - Let (E, ⊥, ⊕, 0, 1) be a lattice effect algebra and τi its interval topology. In this work we show that if the operation ⊕ is continuous with respect to τi, then τi is Hausdorff. In addition, we also show that if (E, ⊥, ⊕, 0, 1) is a complete M V-effect algebra and τi is a Hausdorff topology, then the operations ⊕, ⊖, ∨ and ∧ are τi continuous.

AB - Let (E, ⊥, ⊕, 0, 1) be a lattice effect algebra and τi its interval topology. In this work we show that if the operation ⊕ is continuous with respect to τi, then τi is Hausdorff. In addition, we also show that if (E, ⊥, ⊕, 0, 1) is a complete M V-effect algebra and τi is a Hausdorff topology, then the operations ⊕, ⊖, ∨ and ∧ are τi continuous.

KW - Atom

KW - Continuity of operations

KW - Interval topology

KW - Lattice effect algebra

KW - M V-effect algebra

UR - https://www.scopus.com/pages/publications/67349218996

U2 - 10.1016/j.aml.2009.01.008

DO - 10.1016/j.aml.2009.01.008

M3 - 文章

AN - SCOPUS:67349218996

SN - 0893-9659

VL - 22

SP - 1003

EP - 1006

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 7

ER -

Interval topology of lattice effect algebras

Abstract

Keywords

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