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On locally solid topological lattice groups
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 963-973 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $(G,\tau )$ be a commutative Hausdorff locally solid lattice group. In this paper we prove the following: (1) If $(G,\tau )$ has the $A$(iii)-property, then its completion $(\widehat{G},\hat{\tau })$ is an order-complete locally solid lattice group. (2) If $G$ is order-complete and $\tau $ has the Fatou property, then the order intervals of $G$ are $\tau $-complete. (3) If $(G,\tau )$ has the Fatou property, then $G$ is order-dense in $\widehat{G}$ and $(\widehat{G},\hat{\tau })$ has the Fatou property. (4) The order-bound topology on any commutative lattice group is the finest locally solid topology on it. As an application, a version of the Nikodym boundedness theorem for set functions with values in a class of locally solid topological groups is established.
Let $(G,\tau )$ be a commutative Hausdorff locally solid lattice group. In this paper we prove the following: (1) If $(G,\tau )$ has the $A$(iii)-property, then its completion $(\widehat{G},\hat{\tau })$ is an order-complete locally solid lattice group. (2) If $G$ is order-complete and $\tau $ has the Fatou property, then the order intervals of $G$ are $\tau $-complete. (3) If $(G,\tau )$ has the Fatou property, then $G$ is order-dense in $\widehat{G}$ and $(\widehat{G},\hat{\tau })$ has the Fatou property. (4) The order-bound topology on any commutative lattice group is the finest locally solid topology on it. As an application, a version of the Nikodym boundedness theorem for set functions with values in a class of locally solid topological groups is established.
Classification : 28B15, 46A40, 54H11
Keywords: topological completion; locally solid $\ell $-group; topological continuity; Fatou property; order-bound topology 
@article{CMJ_2007_57_3_a13,
     author = {Khan, Abdul Rahim and Rowlands, Keith},
     title = {On locally solid topological lattice groups},
     journal = {Czechoslovak Mathematical Journal},
     pages = {963--973},
     year = {2007},
     volume = {57},
     number = {3},
     mrnumber = {2356933},
     zbl = {1174.54025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a13/}
}
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Khan, Abdul Rahim; Rowlands, Keith. On locally solid topological lattice groups. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 963-973. http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a13/