Ideal convergence and divergence of nets in $(\ell )$-groups

Title:

Ideal convergence and divergence of nets in $(\ell )$-groups

Creator:

Boccuto, Antonio, Dimitriou, Xenofon, and Nikolaos

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:7ba022ab-a503-4d6d-99de-fac656f9ea3f
uuid:7ba022ab-a503-4d6d-99de-fac656f9ea3f

Subject:

set, $(\ell )$-group, ideal, ideal order, $(D)$-convergence, and ideal convergence

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper we introduce the ${\mathcal I}$- and ${\mathcal I}^*$-convergence and divergence of nets in $(\ell )$-groups. We prove some theorems relating different types of convergence/divergence for nets in $(\ell )$-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 ${\mathcal I}^*$-convergence/divergence implies ${\mathcal I}$-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. Finally we pose some open problems.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1073-1083

Source:

Czechoslovak Mathematical Journal | 2012 Volume:62 | Number:4

Harvested from:

CDK

Metadata only:

false