In this paper we introduce the I- and I^*-convergence and divergence of nets in l-groups. We prove some theorems relating different types of convergence/divergence for nets in l-group setting, in relation with ideals. We consider both order and (D)-convergence. By using basic properties of order sequences, some fundamental properties, Cauchy-type characterizations and comparison results are derived. We prove that I^-convergence/divergence implies I-convergence/divergence for every ideal, admissible for the set of indexes with respect to which the net involved is directed, and we investigate a class of ideals for which the converse implication holds.
Ideal convergence and divergence of nets in l-groups
BOCCUTO, Antonio;
2012
Abstract
In this paper we introduce the I- and I^*-convergence and divergence of nets in l-groups. We prove some theorems relating different types of convergence/divergence for nets in l-group setting, in relation with ideals. We consider both order and (D)-convergence. By using basic properties of order sequences, some fundamental properties, Cauchy-type characterizations and comparison results are derived. We prove that I^-convergence/divergence implies I-convergence/divergence for every ideal, admissible for the set of indexes with respect to which the net involved is directed, and we investigate a class of ideals for which the converse implication holds.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
