A topology on lattice-ordered groups
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Authors
Huanrong Wu
- College of Mathematics and Econometrics, Hunan University, Changsha 410082, China.
Qingguo Li
- College of Mathematics and Econometrics, Hunan University, Changsha 410082, China.
Bin Yu
- College of Mathematics and Econometrics, Hunan University, Changsha 410082, China.
Abstract
We introduce the concept of the strong-positive cone in a lattice-ordered group \((G,\leq,\cdot)\) and define the continuous lattice-ordered group. We also investigate the \(C\)-topology and bi-\(C\)-topology given on a lattice-ordered group. The main results obtained in this paper are as follows: (1) \((G,\leq,\cdot)\) is a continuous lattice-ordered group if and only if \((G,\leq)\) is a continuous poset; (2) for the bi-\(C\)-topology \(\tau\) in a continuous lattice-ordered group \((G,\leq,\cdot)\), \((G,\cdot,\tau)\) is a topological group and \((G,\leq,\tau)\) is a topological lattice.
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ISRP Style
Huanrong Wu, Qingguo Li, Bin Yu, A topology on lattice-ordered groups, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 5, 701--712
AMA Style
Wu Huanrong, Li Qingguo, Yu Bin, A topology on lattice-ordered groups. J. Nonlinear Sci. Appl. (2018); 11(5):701--712
Chicago/Turabian Style
Wu, Huanrong, Li, Qingguo, Yu, Bin. "A topology on lattice-ordered groups." Journal of Nonlinear Sciences and Applications, 11, no. 5 (2018): 701--712
Keywords
- Lattice-ordered group
- continuous
- topology
- topological group
- topological lattice
MSC
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