Bulletin of the London Mathematical Society ( IF 0.787 ) Pub Date : 2021-05-04 , DOI: 10.1112/blms.12494
Pantelis E. Eleftheriou

Let $G$ be a group definable in a weakly o‐minimal non‐valuational structure $M$. Then $G / G 00$, equipped with the logic topology, is a compact Lie group, and if $G$ has finitely satisfiable generics, then $dim ( G / G 00 ) = dim ( G )$. Our main technical result is that $G$ is a dense subgroup of a group definable in the canonical o‐minimal extension of $M$.

$G$ 是在弱最小非评估结构中可定义的组 $中号$。然后$G / G 00$配备了逻辑拓扑的是一个紧凑的Lie组，如果 $G$ 具有可满足要求的泛型，那么 $暗淡 （ G / G 00 ） = 暗淡 （ G ）$。我们的主要技术成果是$G$ 是在的典范o-最小扩展中可定义的组的密集子组 $中号$

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