A remark on nearness spaces

TL;DR

This paper proves that the category of nearness spaces is bireflective within the category of merotopic spaces, using Zorn's Lemma as a key tool instead of traditional transfinite induction.

Contribution

It provides a new proof of a known categorical relationship employing Zorn's Lemma, offering an alternative to existing methods.

Findings

Established bireflectivity of nearness spaces in merotopic spaces

Used Zorn's Lemma for the proof, differing from traditional approaches

Simplified the proof structure with set-theoretic techniques

Abstract

We give a proof of the well-known fact that the category of nearness spaces is bireflective in the category of merotopic spaces which uses Zorn's Lemma instead of the usual construction by transfinite induction.