Continuous Maps on Digital Simple Closed Curves
نویسنده
چکیده
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: 1) A digital simple closed curve S of more than 4 points is not contractible, i.e., its identity map is not nullhomotopic in S ; 2) Let X and Y be digital simple closed curves, each symmetric with respect to the origin, such that 5 |> | Y (where | | Y is the number of points in Y ). Let Y X f : be a digitally continuous antipodal map. Then f is not nullhomotopic in Y ; 3) Let S be a digital simple closed curve that is symmetric with respect to the origin. Let Z S f : be a digitally continuous map. Then there is a pair of antipodes S x x } , { such that 1 | ) ( ) ( | x f x f .
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