Initial λ-compactness in linearly ordered spaces

Abstract

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

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