TL;DR
This paper investigates the integration of Busemann's synthetic metric space theory with synthetic differential geometry utilizing nilpotent elements, aiming to unify two geometric frameworks.
Contribution
It introduces a novel approach combining metric space theory with synthetic differential geometry based on nilpotent elements.
Findings
Unified framework for metric spaces and differential geometry
Potential applications in geometric analysis and topology
Foundations for further theoretical development
Abstract
We explore how the synthetic theory of metric spaces (Busemann) can coexist with synthetic differential geometry in the sense based on nilpotent elements in the number line.
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Taxonomy
TopicsAdvanced Topics in Algebra · Mathematics and Applications · Geometric and Algebraic Topology