Some limit and Dieudonné-type theorems in the setting of (ℓ)-groups with respect to filter convergence are proved, extending earlier results.
In this paper we introduce the - and -convergence and divergence of nets in -groups. We prove some theorems relating different types of convergence/divergence for nets in -group setting, in relation with ideals. We consider both order and -convergence. By using basic properties of order sequences, some fundamental properties, Cauchy-type characterizations and comparison results are derived. We prove that -convergence/divergence implies -convergence/divergence for every ideal, admissible for...
Page 1