Finite basis for analytic strong n-gaps

TL;DR

This paper characterizes a finite set of minimal analytic n-gaps that are not countably separated and proves that any such gap contains one from this list, providing a comprehensive classification.

Contribution

It introduces a finite list of minimal analytic n-gaps and establishes their universality among non-countably separated gaps.

Findings

Finite list of minimal analytic n-gaps identified.

Every non-countably separated analytic n-gap contains a gap from this list.

Provides a classification framework for analytic n-gaps.

Abstract

We identify the finite list of minimal analytic n-gaps which are not countably separated, and we prove that every analytic n-gap which is not countably separated contains a gap from our finite list.