External characterization of I-favorable spaces

TL;DR

This paper characterizes I-favorable spaces with respect to co-zero sets using spectral and internal methods, and explores their properties under products and embeddings, revealing new structural insights.

Contribution

It introduces spectral and internal characterizations of I-favorable spaces with respect to co-zero sets and examines their behavior under products and embeddings.

Findings

Product of compact I-favorable spaces is I-favorable.

C*-embedded I-favorable subspaces of extremally disconnected spaces are extremally disconnected.

Provides new characterizations of I-favorable spaces.

Abstract

We provide both a spectral and an internal characterizations of arbitrary I-favorable spaces with respect to co-zero sets. As a corollary we establish that any product of compact I-favorable spaces with respect to co-zero sets is also I-favorable with respect to co-zero sets. We also prove that every C*-embedded I-favorable with respect to co-zero sets subspace of an extremally disconnected space is extremally disconnected.