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- W2126566290 abstract "We consider an arbitrary topological group $G$ definable in a structure $mathcal M$, such that some basis for the topology of $G$ consists of sets definable in $mathcal M$. To each such group $G$ we associate a compact $G$-space of partial types $S^mu_G(M)={p_mu:pin S_G(M)}$ which is the quotient of the usual type space $S_G(M)$ by the relation of two types being infinitesimally close to each other. In the o-minimal setting, if $p$ is a definable type then it has a corresponding definable subgroup $Stab_mu(p)$, which is the stabilizer of $p_mu$. This group is nontrivial when $p$ is unbounded in the sense of $mathcal M$; in fact it is a torsion-free solvable group. Along the way, we analyze the general construction of $S^mu_G(M)$ and its connection to the Samuel compactification of topological groups." @default.
- W2126566290 created "2016-06-24" @default.
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- W2126566290 date "2014-09-18" @default.
- W2126566290 modified "2023-10-16" @default.
- W2126566290 title "Topological groups, mu-types and their stabilizers" @default.
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