Contractibility of the digital $n$-space

Sayaka Hamada
DOI: https://doi.org/10.4995/agt.2015.1826

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

M. Fujimoto, S. Takigawa, J. Dontchev, H. Maki and T. Noiri, The topological structures and groups of digital n-spaces, Kochi J. Math. 1 (2006), 31-55.

S. Hamada and T. Hayashi, Fuzzy topological structures of low dimensional digital spaces, Journal of Fuzzy Mathematics 20, no. 1 (2012), 15-23.

E. D. Khalimsky, On topologies of generalized segments, Soviet Math. Doklady 10 (1969), 1508-1511.

E. Khalimsky, R. Kopperman and P. R. Meyer, Computer graphics and connected topologies on finite ordered sets, Topology Appl. 36 (1990), 1-17. (http://dx.doi.org/10.1016/0166-8641(90)90031-V)

T. Y. Kong, R. Kopperman and P. R. Meyer, A topological approach to digital topology, Am. Math. Monthly 98 (1991), 901-917. (http://dx.doi.org/10.2307/2324147)

E. H. Kronheimer, The topology of digital images, Topology Appl. 46 (1992), 279-303. (http://dx.doi.org/10.1016/0166-8641(92)90019-V)

G. Raptis, Homotopy theory of posets, Homology, Homotopy and Applications 12, no. 2 (2010), 211-230. (http://dx.doi.org/10.4310/HHA.2010.v12.n2.a7)

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