# Difference between revisions of "Publications/boutry.22.jmiv"

## Abstract

In this paper, we prove that when a ${\displaystyle n}$-D cubical set is continuously well-composed (CWC), that is, when the boundary of its continuous analog is a topological ${\displaystyle (n-1)}$-manifold, then it is digitally well-composed (DWC)which means that it does not contain any critical configuration. We prove this result thanks to local homology. This paper is the sequel of a previous paper where we proved that DWCness does not imply CWCness in 4D.

## Bibtex (lrde.bib)

```@Article{	  boutry.22.jmiv,
author	= {Nicolas Boutry and Rocio Gonzalez-Diaz and Laurent Najman
and Thierry G\'eraud},
title		= {Continuous Well-Composedness implies Digital
Well-Composedness in \$n\$-D},
journal	= {Journal of Mathematical Imaging and Vision},
volume	= {64},
number	= {2},
pages		= {131--150},
month		= jan,
year		= {2022},
abstract	= {In this paper, we prove that when a \$n\$-D cubical set is
continuously well-composed (CWC), that is, when the
boundary of its continuous analog is a topological
\$(n-1)\$-manifold, then it is digitally well-composed (DWC),
which means that it does not contain any critical
configuration. We prove this result thanks to local
homology. This paper is the sequel of a previous paper
where we proved that DWCness does not imply CWCness in
4D.},
doi		= {10.1007/s10851-021-01058-8}
}```