ultrahomogeneous

English

Etymology

From ultra- +‎ homogeneous.

Adjective

ultrahomogeneous (not comparable)

1. (mathematics) Such that every isomorphism between finitely generated substructures extends to an automorphism of itself.
   • 2016, J. Jonušas, J. D. Mitchell, “Topological 2-generation of automorphism groups of countable ultrahomogeneous graphs”, in arXiv‎^[1]:

     We show that if $\Gamma$ is ultrahomogeneous, then $\operatorname {Aut} (\Gamma )$ has 2-generated dense subgroups, and that under certain conditions given $f\in \operatorname {Aut} (\Gamma )$ there exists $g\in \operatorname {Aut} (\Gamma )$ such that the subgroup generated by $f$ and $g$ is dense.