Inverse Systems and I-Favorable Spaces

TL;DR

This paper characterizes I-favorable compact spaces as limits of inverse systems of metrizable spaces with skeletal bonding maps, providing a new perspective on their structure.

Contribution

It establishes a precise equivalence between I-favorable spaces and inverse limits of specific inverse systems, advancing understanding of their topological properties.

Findings

I-favorable spaces are exactly limits of $\sigma$-complete inverse systems of metrizable spaces

Skeletal bonding maps characterize the structure of I-favorable spaces

Provides a new framework for analyzing compact spaces via inverse systems

Abstract

A compact space X is I-favorable if, and only if X can be representing as a limit of $\sigma$-complete inverse system of compact metrizable spaces with skeletal bonding maps.