Contractibility of the digital $n$-space

Sayaka Hamada

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.

Subject classification

14F35; 54B10.

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References

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