2020/02/12 by Claude Laflamme, Maurice Pouzet, Laflamme, Claude +5 · 1 citation
Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Limits and Structures in Graph Theory #Logic (math.LO) #math.CO #math.GR #math.LO
paper · pdf · doi:10.48550/arxiv.2002.04771
arxiv created 2020/02/12 · openalex publication_date 2020/02/12 · arxiv updated 2020/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a subgroup of the symmetric group \mathfrak S(U) of all permutations of a countable set U. Let G be the topological closure of G in the function topology on UU. We initiate the study of the poset G[U]:=\f[U]| f∈ G\ of images of the functions in G, being ordered under inclusion. This set G[U] of subsets of the set U will be called the poset of copies for the group G. A denomination being justified by the fact that for every subgroup G of the symmetric group \mathfrak S(U) there exists a homogeneous relational structure R on U such that G is the set of embeddings of the homogeneous structure R into itself and G[U] is the set of copies of R in R and that the set of bijections G∩ \mathfrak S(U) of U to U forms the group of automorphisms of R.