A categorical perspective on extended metric-topological spaces

Enrico Pasqualetto; Timo Schultz; Janne Taipalus

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arXiv · 2601.07505

A categorical perspective on extended metric-topological spaces

Enrico Pasqualetto·Timo Schultz·Janne Taipalus

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Abstract

Motivated by the analysis and geometry of metric-measure structures in infinite dimensions, we study the category of extended metric-topological spaces, along with many of its distinguished subcategories (such as the one of compact spaces). One of the main achievements is the proof of the bicompleteness (i.e. of the existence of all small limits and colimits) of the aforementioned categories.

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Enrico Pasqualetto, Timo Schultz, Janne Taipalus. 2026-01-12. A categorical perspective on extended metric-topological spaces. https://arxiv.org/abs/2601.07505

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