2023/01/16 by Vladimir Kadets, Kadets, Vladimir, Olesia Zavarzina +1 · 1 citation
Decision Sciences · Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Fuzzy and Soft Set Theory
paper · pdf · doi:10.48550/arxiv.2301.06589
openalex publication_date 2023/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We address pairs (X, Y) of metric spaces with the following property: for every mapping f: X → Y the existence of points x, y ∈ X with d(f(x),f(y)) > d(x,y) implies the existence of \widetildex, \widetildey∈ X for which d(f(\widetildex),f(\widetildey)) < d(\widetildex,\widetildey). We give sufficient conditions for this property and for its uniform version in terms of finite ε-nets and finite ε-separated subsets.