# On the topology and the boundary of N-dimensional RCD(K,N) spaces

## TL;DR

This paper investigates the topological structure and boundary properties of N-dimensional RCD(K,N) spaces, establishing regularity, stability, and boundary behavior under convergence, thus advancing the understanding of these metric measure spaces.

## Contribution

It introduces the concept of a boundary for RCD(K,N) spaces and analyzes its properties, including stability under Gromov-Hausdorff convergence, with results on topological regularity.

## Key findings

- Established topological regularity of RCD(K,N) spaces
- Defined and studied the boundary of RCD(K,N) spaces
- Proved stability of boundary properties under Gromov-Hausdorff convergence

## Abstract

We establish topological regularity and stability of N-dimensional RCD(K,N) spaces (up to a small singular set), also called non-collapsed RCD(K,N) in the literature. We also introduce the notion of a boundary of such spaces and study its properties, including its behavior under Gromov-Hausdorff convergence.