Indestructibility of compact spaces

Abstract

In this article we investigate which compact spaces remain compact under countably closed forcing. We prove that, assuming the Continuum Hypothesis, the natural generalizations to ${\omega }_1$-sequences of the selection principle and topological game versions of the Rothberger property are not equivalent, even for compact spaces. We also show that Tall and Usuba's "${\aleph }_1$-Borel Conjecture" is equiconsistent with the existence of an inaccessible cardinal.

18 pages

References in corpus (1)

• Set-theoretic problems concerning Lindelof spaces

Cited by in corpus (2)

• Productively Lindelof and Indestructibly Lindelof Spaces
• Some observations on compact indestructible spaces