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About: Grid cell topology     Goto   Sponge   NotDistinct   Permalink

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The grid cell topology is studied in digital topology as part of the theoretical basis for (low-level) algorithms in computer image analysis or computer graphics. The elements of the n-dimensional grid cell topology (n ≥ 1) are all n-dimensional grid cubes and their k-dimensional faces ( for 0 ≤ k ≤ n−1); between these a partial order A ≤ B is defined if A is a subset of B (and thus also dim(A) ≤ dim(B)). The grid cell topology is the Alexandrov topology (open sets are up-sets) with respect to this partial order. (See also poset topology.)