# Classification of metric spaces with infinite asymptotic dimension

## TL;DR

This paper introduces a new geometric property called complementary-finite asymptotic dimension (coasdim), extending the theory of asymptotic dimension with new invariants and theorems for metric space classification.

## Contribution

It defines coasdim, proves its invariance under coarse equivalences, and establishes key theorems analogous to those for asymptotic dimension.

## Key findings

- Coasdim is a coarse invariant.
- The paper proves a union theorem for coasdim.
- A Hurewicz-type theorem for coasdim is established.

## Abstract

We introduce a geometric property complementary-finite asymptotic dimension (coas- dim). Similar with asymptotic dimension, we prove the corresponding coarse invariant theorem, union theorem and Hurewicz-type theorem.