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This paper concerns the problem of ordering geometrical objects, which have the structure of finite cellular spaces. We introduce cellular codes, cellular indices, and (k,l)-sizes and apply them to ordering 2-cells, plane curves, and projections of knots. Results of this paper can be applied (1) to ordering other geometrical objects with cellular space structures, (2) in psychological and computer tests for comparison of complexity of geometrical objects, and (3) to ordering objects with fractal and chaotic structure, which admit approximation by cellular spaces.

Ordering Cellular Spaces with Application to Curves and Knots