Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Lipschitz-free spaces over uniformly discrete metric spaces are 3-Schur

Marek Cúth, Ondřej F. K. Kalenda

Abstract

We prove that the Lipschitz-free space over any uniformly discrete metric space has the 3-Schur property

Lipschitz-free spaces over uniformly discrete metric spaces are 3-Schur

Abstract

We prove that the Lipschitz-free space over any uniformly discrete metric space has the 3-Schur property

Paper Structure

This paper contains 5 sections, 13 theorems, 44 equations.

Table of Contents

  1. Introduction
  2. On quantification of the Schur property
  3. Auxilliary results
  4. Proof of Theorem \ref{['T:main']}
  5. Proofs of Theorem \ref{['t:0hyp']} and its corollary

Key Result

Theorem 1.1

Let $M$ be a uniformly discrete metric space. Then $\mathcal{F}(M)$ is $3$-Schur. Moreover, the constant $3$ is optimal. $\blacktriangleleft$$\blacktriangleleft$

Theorems & Definitions (24)

  • Theorem 1.1
  • Theorem 1.4
  • Corollary 1.5
  • Lemma 2.1
  • Proposition 2.2
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • ...and 14 more