2023/04/07 by Viktoriia Bilet, Oleksiy Dovgoshey, Bilet, Viktoriia +1 · 2 citations
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Metric Geometry (math.MG) #Primary 54E35 #Secondary 20M05
paper · pdf · doi:10.48550/arxiv.2304.03822
openalex publication_date 2023/04/07 · openalex created_date 2023/04/13 · openalex updated_date 2026/07/28
The group of combinatorial self-similarities of a pseudometric space (X, d) is the maximal subgroup of the symmetric group Sym (X) whose elements preserve the four-point equality d(x,y)=d(u,v). Let us denote by IP the class of all pseudometric spaces (X, d) for which every combinatorial self-similarity Φ\colon~X~→~X satisfies the equality d(x, Φ(x))=0, but all permutations of metric reflection of (X, d) are combinatorial self-similarities of this reflection. The structure of IP spaces is fully described.