A topology on lattice-ordered groups

Volume 11, Issue 5, pp 701--712 http://dx.doi.org/10.22436/jnsa.011.05.10
Publication Date: April 05, 2018 Submission Date: April 13, 2017 Revision Date: February 03, 2018 Accteptance Date: March 01, 2018

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


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