IJPAM: Volume 70, No. 2 (2011)

IDEAL EXHAUSTIVENESS, CONTINUITY AND
$(\alpha)$-CONVERGENCE FOR LATTICE
GROUP-VALUED FUNCTIONS

A. Boccuto$^1$, X. Dimitriou$^2$, N. Papanastassiou$^3$, W. Wilczyński$^4$
$^1$Department of Mathematics and Computer Sciences
University of Perugia
1, Via Vanvitelli, I-06123 Perugia, ITALY
$^{2,3}$Department of Mathematics
University of Athens
Panepistimiopolis, Athens, 15784, GREECE
$^4$Faculty of Mathematics and Computer Sciences
University of Łódż
Banacha 22, PL-90238, Łódż, POLAND


Abstract. We examine some fundamental properties of ${\mathcal I}$-exhaustiveness, previously studied in the real case in [#!PPW!#], in the context of $(\ell)$-groups with respect to $(D)$-convergence and we answer to an open problem posed by V. Gregoriades and N. Papanastassiou in [#!GP!#].

Received: April 8, 2011

AMS Subject Classification: 28B15, 54A20

Key Words and Phrases: $(\ell)$-group, ideal, admissible ideal, good ideal, continuous convergence, (global) equicontinuity, (global) even continuity, ideal continuity, (global) ideal $(D)$-convergence, (global) ideal exhaustiveness, weak ideal exhaustiveness

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 2