Continuous Maps on Digital Simple Closed Curves

Laurence Boxer

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DOI: 10.4236/am.2010.15050                

Abstract

We give digital analogues of classical theorems of topology for continuous functions defined on spheres, for digital simple closed curves. In particular, we show the following. ? A digital simple closed curve of more than 4 points is not contractible, i.e., its identity map is not nullhomotopic in . ? Let and be digital simple closed curves, each symmetric with respect to the origin, such that (where is the number of points in ). Let be a digitally continuous antipodal map. Then is not nullho- motopic in . ? Let be a digital simple closed curve that is symmetric with respect to the origin. Let be a digitally continuous map. Then there is a pair of antipodes such that .

Keywords

Digital Image, Digital Topology, Homotopy, Antipodal Point

Conflicts of Interest

The authors declare no conflicts of interest.

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