u tau-convergence in locally solid vector lattices

Dabboorasad Y. A., EMELYANOV E., Marabeh M. A. A.

POSITIVITY, vol.22, no.4, pp.1065-1080, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.1007/s11117-018-0559-4
  • Journal Name: POSITIVITY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1065-1080
  • Keywords: Banach lattice, Vector lattice, ut-convergence, ut-topology, uo-convergence, un-convergence, un-topology, UNBOUNDED ORDER CONVERGENCE, BANACH-LATTICES
  • Middle East Technical University Affiliated: Yes

Abstract

Let be a net in a locally solid vector lattice ; we say that is unbounded -convergent to a vector if for all . In this paper, we study general properties of unbounded -convergence (shortly -convergence). -convergence generalizes unbounded norm convergence and unbounded absolute weak convergence in normed lattices that have been investigated recently. We introduce -topology and briefly study metrizability and completeness of this topology.