Michael Spaces and Ultrafilters

TL;DR

This paper introduces the concept of Michael ultrafilters and constructs a Michael space assuming the existence of a selective ultrafilter and certain cardinal invariants, linking topology and set theory.

Contribution

It defines Michael ultrafilters and demonstrates the construction of a Michael space under specific set-theoretic assumptions, advancing the understanding of these spaces.

Findings

Construction of a Michael space under set-theoretic assumptions

Introduction of the notion of Michael ultrafilter

Connection between ultrafilters and topological properties

Abstract

A Michael space is a Lindel\"of space which has a non-Lindel\"of product with the Baire space. In this work, we present the notion of Michael ultrafilter and we use it to construct a Michael space under the existence of a selective ultrafilter and $\max \{ \mathfrak{b}, \mathfrak{g} \} =\mathfrak{d}$.