Contractibility of the digital $n$-space

Abstract

The aim of this paper is to prove a known fact that the digital line is cotractible. Hence we have that the digital space $({\bf Z}^{n}, \kappa^{n})$ is also cotractible where $({\bf Z}^{n}, \kappa^{n})$ is $n$ products of the digital line $({\bf Z}, \kappa)$. This is a fundamental property of homotopy theory.

Keywords

• Khalimsky topology
• digital $n$-space
• contractible
• homotopy.