Contractibility of the digital $n$-space

Sayaka Hamada

doi:10.4995/agt.2015.1826

Authors

Sayaka Hamada National Institute of Technology

DOI:

https://doi.org/10.4995/agt.2015.1826

Keywords:

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

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.

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References

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