Extremally Disconnected Groups of Measurable Cardinality

TL;DR

This paper constructs a nondiscrete Hausdorff extremally disconnected topological group with a measurable cardinality, expanding the understanding of such groups in set-theoretic topology.

Contribution

It provides the first known construction of extremally disconnected groups of measurable cardinality, linking set theory and topological group theory.

Findings

Existence of extremally disconnected groups of measurable cardinality

Construction method for such groups

Bridges set theory and topological group concepts

Abstract

Given an arbitrary measurable cardinal $\kappa$, a nondiscrete Hausdorff extremally disconnected topological group of cardinality $\kappa$ is constructed.