  Universal representation of geometric patterns of disordered matters is
investigated with the aid of general topology. By utilizing the result obtained
in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that
any patterns can be represented by a specific topological space, a construction
of topological representation of patterns using Cantor set is shown. The
obtained topological representations are then demonstrated by the contractions
that characterize the self-similarity of Cantor set. For some practical
geometric patterns, e.g., network, dendritic, and clusterized patterns, their
topological representations are focused on.
