ultrahomogeneous

ultrahomogeneous

English

Etymology

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:

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