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Construction of topological representation of geometric patterns using Cantor self-similar set
Shousuke Ohmori, Yoshihiro Yamazaki, Tomoyuki Yamamoto +1
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. Oh…
Universal topological representation of geometric patterns
Shousuke Ohmori, Yoshihiro Yamazaki, Tomoyuki Yamamoto +1
We discuss here geometric structures of condensed matters by means of a fundamental topological method. Any geometric pattern can be universally represented by a decomposition spac…
Topological characterization of network structures of aggregates of atoms
Shousuke Ohmori, Tomoyuki Yamamoto, Akihiko Kitada
Two distinct structures of aggregates of atoms connected by anisotropic bonds with a network configuration are discussed from the viewpoint of a point set topology. A specific topo…
On the Existence of a Self-Similar Coarse Graining of a Self-Similar Space
Akihiko Kitada, Tomoyuki Yamamoto, Tsuyoshi Yoshioka +1
A topological space homeomorphic to a self-similar space is demonstrated to be self-similar. There exists a self-similar space whose coarse graining is homeomorphic to . The…