{
  "id": "2301.06589",
  "version": "v1",
  "published": "2023-01-16T20:11:02.000Z",
  "updated": "2023-01-16T20:11:02.000Z",
  "title": "Plastic pairs of metric spaces",
  "authors": [
    "Vladimir Kadets",
    "Olesia Zavarzina"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We address pairs $(X, Y)$ of metric spaces with the following property: for every mapping $f: X \\to Y$ the existence of points $x, y \\in X$ with $d(f(x),f(y)) > d(x,y)$ implies the existence of $\\widetilde{x}, \\widetilde{y}\\in X$ for which $d(f(\\widetilde{x}),f(\\widetilde{y})) < d(\\widetilde{x},\\widetilde{y})$. We give sufficient conditions for this property and for its uniform version in terms of finite $\\varepsilon$-nets and finite $\\varepsilon$-separated subsets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-16T20:11:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metric spaces",
      "plastic pairs",
      "address pairs",
      "sufficient conditions",
      "uniform version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}