CH and the Moore-Mrowka Problem

TL;DR

This paper demonstrates a model of set theory where the Continuum Hypothesis holds and certain topological properties, like being C-closed and sequential, are consistent with regular spaces of hereditarily countable π-character and countable tightness.

Contribution

It establishes the consistency of CH with topological properties such as C-closedness and sequentiality in compact spaces of countable tightness.

Findings

CH is consistent with all regular spaces of hereditarily countable π-character being C-closed

A model where CH holds and compact Hausdorff spaces of countable tightness are sequential

Provides a set-theoretic framework linking CH with topological properties

Abstract

We show that the Continuum Hypothesis is consistent with all regular spaces of hereditarily countable $\pi$-character being C-closed. This gives us a model of ZFC in which the Continuum Hypothesis holds and compact Hausdorff spaces of countable tightness are sequential.