A remark on nearness spaces
Jan-David Hardtke

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.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Differential Geometry Research · Advanced Banach Space Theory
