Compact spaces of the first Baire class that have open finite degree

TL;DR

This paper introduces the concept of open degree for compact spaces and proves that separable Rosenthal compact spaces of a fixed degree n have a finite basis, advancing understanding of their structure.

Contribution

It defines the open degree of compact spaces and establishes a finite basis result for separable Rosenthal compact spaces of degree n.

Findings

Separable Rosenthal compact spaces of degree n have a finite basis.

Introduction of the open degree concept for compact spaces.

Finite basis property holds for all natural numbers n.

Abstract

We introduce the open degree of a compact space, and we show that for every natural number n, the separable Rosenthal compact spaces of degree n have a finite basis.