Complete topological classification of Baire spaces functions on ordinals

TL;DR

This paper provides a comprehensive topological classification of Baire function spaces defined on ordinal segments, specifically focusing on the spaces of Baire functions with pointwise convergence topology.

Contribution

It offers the first complete topological classification of Baire function spaces on ordinal segments, expanding understanding of their structure.

Findings

Complete topological classification of Baire function spaces on ordinals

Identification of topological invariants for these spaces

Clarification of the relationship between ordinal segments and function space topology

Abstract

The paper considers the spaces $B_p[1, \alpha]$ of all Baire functions $x\colon [1,\alpha]\to \mathbb{R}$, defined on segments of ordinals $[1,\alpha]$ and endowed with the topology of pointwise convergence. A complete topological classification of these spaces is given