Contractibility of the digital $n$-space

Sayaka Hamada

Japan

National Institute of Technology

Submitted: 2013-11-04

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Accepted: 2014-09-23

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Published: 2015-01-28

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

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

Supporting agencies:

This research was not funded

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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