On non-separable growths of omega supporting measures

TL;DR

This paper provides ZFC examples of compactifications of omega with nonseparable remainders that support strictly positive measures, advancing understanding of measure-supporting nonseparable spaces.

Contribution

It introduces new ZFC constructions of compactifications with nonseparable, measure-supporting remainders, expanding the class of known examples.

Findings

Existence of nonseparable remainders with positive measures in ZFC

Construction of compactifications with these properties

Advancement in understanding measure-supporting nonseparable spaces

Abstract

We present several $\mathsf{ZFC}$ examples of compactifications $\gamma\omega$ of $\omega$ such that their remainders $\gamma\omega\backslash\omega$ are nonseparable and carry strictly positive measures.