English

Initial \lambda-compactness in linearly ordered spaces

General Topology 2013-07-05 v3

Abstract

We show that a linearly ordered topological space is initially \lambda-compact if and only if it is \lambda-bounded, that is, every set of cardinality λ\leq \lambda has compact closure. As a consequence, every product of initially \lambda-compact linearly ordered topological spaces is initially \lambda-compact.

Keywords

Cite

@article{arxiv.1306.1715,
  title  = {Initial \lambda-compactness in linearly ordered spaces},
  author = {Paolo Lipparini},
  journal= {arXiv preprint arXiv:1306.1715},
  year   = {2013}
}

Comments

v.3 simplified the proof of (4) implies (5) in the Theorem

R2 v1 2026-06-22T00:29:53.167Z