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On locally solid topological lattice groups

Abdul Rahim KhanKeith Rowlands — 2007

Czechoslovak Mathematical Journal

Let ( G , τ ) be a commutative Hausdorff locally solid lattice group. In this paper we prove the following: (1) If ( G , τ ) has the A (iii)-property, then its completion ( G ^ , τ ^ ) is an order-complete locally solid lattice group. (2) If G is order-complete and τ has the Fatou property, then the order intervals of G are τ -complete. (3) If ( G , τ ) has the Fatou property, then G is order-dense in G ^ and ( G ^ , τ ^ ) has the Fatou property. (4) The order-bound topology on any commutative lattice group is the finest locally solid topology on...

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