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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…