On the Topological Properties of Quantized Spaces, II. Connectivity and Order of Connectivity
John Mylopoulos, Theodoros E Pavlidis · Journal of the ACM · 1971
A notion of equivalence (c-equivalence) is defined as the counterpart of homeoinorphism for quantized spaces.It is shown that sets with the same number of components and holes are c-equivalent in two-dimensional spaces.Then it is shown that for each arbitrary set there is a set c-equivalent to it with certain "regular" features (rectangular perimeter, holes with diameter one, etc.).