Michael Spaces and Ultrafilters
Arturo Mart\'inez-Celis

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 .
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Banach Space Theory · Advanced Algebra and Logic
