S-spaces and large continuum

TL;DR

This paper demonstrates the consistency of the non-existence of S-spaces and bounds the size of certain compact spaces under large continuum assumptions.

Contribution

It establishes the consistency of no S-spaces with large continuum and bounds the size of compact separable spaces of countable tightness.

Findings

No S-spaces exist under certain set-theoretic assumptions.

Compact separable spaces of countable tightness have size at most continuum.

Provides set-theoretic consistency results related to topological spaces.

Abstract

We prove that it is consistent with large values of the continuum that there are no S-spaces. We also show that we can also have that compact separable spaces of countable tightness have cardinality at most the continuum.