Hausdorff Compactifications

TL;DR

This paper demonstrates that all Hausdorff compactifications can be constructed using a method based on non-standard analysis, simplifying the process of compactification in regular spaces.

Contribution

The authors extend their previous work to show that their non-standard analysis method can generate any Hausdorff compactification.

Findings

All Hausdorff compactifications are obtainable with the proposed method.

The approach simplifies the construction of compactifications.

The method applies to regular spaces.

Abstract

Previously, the authors used the insights of Robinson's non-standard analysis as a powerful tool to extend and simplify the construction of some compactifications of regular spaces. They now show that any Hausdorff compactification is obtainable with their method.