Plastic pairs of metric spaces
Vladimir Kadets, Olesia Zavarzina

TL;DR
This paper investigates pairs of metric spaces with a property that relates the existence of points with increased or decreased distances under any mapping, providing conditions for this property using finite nets and separated sets.
Contribution
It introduces a new property of metric space pairs, called plasticity, and establishes sufficient conditions for this property and its uniform version.
Findings
Characterization of plastic pairs via finite $ ext{epsilon}$-nets.
Conditions for uniform plasticity based on finite separated sets.
Theoretical framework for understanding metric space mappings.
Abstract
We address pairs of metric spaces with the following property: for every mapping the existence of points with implies the existence of for which . We give sufficient conditions for this property and for its uniform version in terms of finite -nets and finite -separated subsets.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Banach Space Theory · Fuzzy and Soft Set Theory
