A topology on lattice-ordered groups

Wu, Huanrong ¹ ; Li, Qingguo ¹ ; Yu, Bin ¹

¹ College of Mathematics and Econometrics, Hunan University, Changsha 410082, China

Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 5, p. 701-712.

Résumé

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.

Détail

DOI : 10.22436/jnsa.011.05.10

Classification : 06F15, 06B35, 54H11
Keywords: Lattice-ordered group, continuous, topology, topological group, topological lattice

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