Geodesic
Locally solid topological lattice-ordered groups
Archivum mathematicum, Tome 51 (2015) no. 2, pp. 107-128

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Locally solid Riesz spaces have been widely investigated in the past several decades; but locally solid topological lattice-ordered groups seem to be largely unexplored. The paper is an attempt to initiate a relatively systematic study of locally solid topological lattice-ordered groups. We give both Roberts-Namioka-type characterization and Fremlin-type characterization of locally solid topological lattice-ordered groups. In particular, we show that a group topology on a lattice-ordered group is locally solid if and only if it is generated by a family of translation-invariant lattice pseudometrics. We also investigate (1) the basic properties of lattice group homomorphism on locally solid topological lattice-ordered groups; (2) the relationship between order-bounded subsets and topologically bounded subsets in locally solid topological lattice-ordered groups; (3) the Hausdorff completion of locally solid topological lattice-ordered groups.
DOI : 10.5817/AM2015-2-107
Classification : 06B35, 06F15, 06F20, 06F30, 20F60, 22A26
Keywords: characterization; Hausdorff completion; lattice homomorphisms; locally solid topological $l$-groups; neighborhood theorem; order-bounded subsets 
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     author = {Hong, Liang},
     title = {Locally solid topological lattice-ordered groups},
     journal = {Archivum mathematicum},
     pages = {107--128},
     publisher = {mathdoc},
     volume = {51},
     number = {2},
     year = {2015},
     doi = {10.5817/AM2015-2-107},
     mrnumber = {3367096},
     zbl = {06487024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2015-2-107/}
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Hong, Liang. Locally solid topological lattice-ordered groups. Archivum mathematicum, Tome 51 (2015) no. 2, pp. 107-128. doi: 10.5817/AM2015-2-107

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