The dependence of the abstract boundary classification on a set of curves II: How the classification changes when the bounded parameter property satisfying set of curves changes

TL;DR

This paper investigates how the classification of boundary points in the abstract boundary framework varies with different sets of curves satisfying the bounded parameter property, extending previous work in the series.

Contribution

It analyzes the impact of changing the set of b.p.p. satisfying curves on the boundary classification, providing insights into the stability of the classification scheme.

Findings

Classification varies with different curve sets

Provides a systematic method to analyze classification changes

Extends previous theoretical framework

Abstract

The abstract boundary uses sets of curves with the bounded parameter property (b.p.p.) to classify the elements of the abstract boundary into regular points, singular points, points at infinity and so on. Building on the material of Part one of this two part series, we show how this classification changes when the set of b.p.p. satisfying curves changes.