Shape in Picture

An object is defined from which digital spaces can be built. It combines the "one-dimensional connectedness" of intervals of reals with a "point-bypoint" quality necessary for constructing algorithms, and thus serves as a foundation for digital topology. Ideas expressed in quotation marks here are given precise meanings. This study considers the Khalimsky line, that is, the integers, equipped with the topology in which a set is open iff whenever it contains an even integer, it also contains its adjacent integers. It is shown that this space and its interval subspaces are those satisfying the conditions mentioned previously. The Khalimsky line is used to study digital connectedness and homotopy.

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