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Vietoris–Rips complex
In topology, the Vietoris–Rips complex, also called the Vietoris complex or Rips complex, is an abstract simplicial complex that can be defined from any metric space ''M'' and distance δ by forming a simplex for every finite set of points that has diameter at most δ. That is, it is a family of finite subsets of ''M'', in which we think of a subset of ''k'' points as forming a (''k'' − 1)-dimensional simplex (an edge for two points, a triangle for three points, a tetrahedron for four points, etc.); if a finite set ''S'' has the property that the distance between every pair of points in ''S'' is at most δ, then we include ''S'' as a simplex in the complex.
==History==
The Vietoris–Rips complex was originally called the Vietoris complex, for Leopold Vietoris, who introduced it as a means of extending homology theory from simplicial complexes to metric spaces.〔; ; ; .〕 After Eliyahu Rips applied the same complex to the study of hyperbolic groups, its use was popularized by , who called it the Rips complex.〔; .〕 The name "Vietoris–Rips complex" is due to .〔.〕
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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