Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A coarse invariant

Addison Fox, Brendon LaBuz, Robert Laskowsky

Abstract

This note extends the invariant defined in "An invariant of metric spaces under bornologous equivalences" to the coarse category.

A coarse invariant

Abstract

This note extends the invariant defined in "An invariant of metric spaces under bornologous equivalences" to the coarse category.

Paper Structure

This paper contains 5 sections, 6 theorems, 1 equation.

Table of Contents

  1. Introduction
  2. Previous construction
  3. Change of basepoint in $\sigma$-stable spaces
  4. The invariant
  5. Some examples

Key Result

Theorem 2.1

Suppose $f:X\to Y$ is a bornologous equivalence between metric spaces. Let $x_0$ be a basepoint of $X$ and set $y_0=f(x_0)$. Suppose $X$ and $Y$ are $\sigma$-stable. Then $\sigma(X,x_0)=\sigma(Y,y_0)$.

Theorems & Definitions (12)

  • Theorem 2.1: MMS, Theorem 3.2
  • Lemma 3.1
  • proof
  • Proposition 3.2
  • proof
  • Theorem 4.1
  • Example 5.1
  • Lemma 5.2
  • proof
  • Example 5.3
  • ...and 2 more