Dimensions of ordered spaces and Lorentzian length spaces
Metric Geometry
2024-03-08 v3
Abstract
After calculating the Dushnik-Miller dimension of Minkowski spaces to be countable infinity, we define a novel notion of dimension for ordered spaces recovering the correct manifold dimension and obtain a corresponding obstruction for the existence of injective monotonous maps between Lorentzian length spaces. Furthermore we induce metrics on Cauchy subsets, relate respective Hausdorff dimensions, prove existence of rushing Cauchy functions with a given Cauchy zero locus and consider collapse phenomena in this setting.
Keywords
Cite
@article{arxiv.2303.11237,
title = {Dimensions of ordered spaces and Lorentzian length spaces},
author = {Olaf Müller},
journal= {arXiv preprint arXiv:2303.11237},
year = {2024}
}
Comments
merged with arXiv:2209.12736 because of close relation and dependency of the contents