English

Order continuity from a topological perspective

Functional Analysis 2017-11-09 v1

Abstract

We study three types of order convergence and related concepts of order continuous maps in partially ordered sets, partially ordered abelian groups and partially ordered vector spaces, respectively. An order topology is introduced such that in the latter two settings under mild conditions order continuity is a topological property. We present a generalisation of the Ogasawara theorem on the structure of the set of order continuous operators.

Keywords

Cite

@article{arxiv.1711.02929,
  title  = {Order continuity from a topological perspective},
  author = {Till Hauser and Anke Kalauch},
  journal= {arXiv preprint arXiv:1711.02929},
  year   = {2017}
}

Comments

35 pages

R2 v1 2026-06-22T22:39:54.383Z