Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Consequences of the existence of ample generics and automorphism groups of homogeneous metric structures (1405.1532v2)

Published 7 May 2014 in math.LO

Abstract: We define a simple criterion for a homogeneous, complete metric structure $X$ that implies that the automorphism group $\mbox{Aut}(X)$ satisfies all the main consequences of the existence of ample generics: it has the small index property, the automatic continuity property, and uncountable cofinality for non-open subgroups. Then we verify it for the Urysohn space $\mbox{U}$, the Lebesgue probability measure algebra $\mbox{MALG}$, and the Hilbert space $\ell_2$, thus proving that $\mbox{Iso}(\mbox{U})$, $\mbox{Aut}(\mbox{MALG})$, $U(\ell_2)$, and $O(\ell_2)$ share these properties. We also formulate a condition for $X$ which implies that every homomorphism of $\mbox{Aut}(X)$ into a separable group $K$ with a left-invariant, complete metric, is trivial, and we verify it for $\mbox{U}$, and $\ell_2$.

Summary

We haven't generated a summary for this paper yet.