Total orders on compact metric spaces and covering dimension
Ivan Mitrofanov

TL;DR
This paper establishes an equivalence between the finite covering dimension of a compact metric space and the existence of a total order with finite snake number, linking topological dimension to order-theoretic properties.
Contribution
It introduces a novel characterization of finite covering dimension via total orders with finite snake number in compact metric spaces.
Findings
Finite covering dimension is equivalent to the existence of a total order with finite snake number.
Provides a new order-theoretic perspective on topological dimension.
Bridges concepts between topology and order theory.
Abstract
We prove that for a compact metric space the property of having finite covering dimension is equivalent to the existence of a total order with finite snake number.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematical Dynamics and Fractals · Advanced Harmonic Analysis Research
