Ultrahomogeneous
adj ·Rare ·Advanced level
Definitions
- 1 Such that every isomorphism between finitely generated substructures extends to an automorphism of itself. not-comparable
"We show that if #92;Gamma is ultrahomogeneous, then #92;operatorname#123;Aut#125;(#92;Gamma) has 2-generated dense subgroups, and that under certain conditions given f#92;in#92;operatorname#123;Aut#125;(#92;Gamma) there exists g#92;in#92;operatorname#123;Aut#125;(#92;Gamma) such that the subgroup generated by f and g is dense."
Example
More examples"We show that if #92;Gamma is ultrahomogeneous, then #92;operatorname#123;Aut#125;(#92;Gamma) has 2-generated dense subgroups, and that under certain conditions given f#92;in#92;operatorname#123;Aut#125;(#92;Gamma) there exists g#92;in#92;operatorname#123;Aut#125;(#92;Gamma) such that the subgroup generated by f and g is dense."
Etymology
From ultra- + homogeneous.
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