Let $G$ be a group definable in a weakly o-minimal non-valuational structure $\mathcal{M}$. 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 $\mathcal{M}$.

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Pillay 对弱 o 极小非估值结构中可定义群的猜想

让 $格$ 是一个可在弱 o 极小非估值结构中定义的组 $\mathcal{米}$. 然后$格/{格}^{00}$，配备逻辑拓扑，是一个紧李群，如果 $格$ 有有限可满足的泛型，那么 $昏暗(格/{格}^{00})=昏暗(格)$. 我们的主要技术成果是$格$ 是一个群的稠密子群，可定义在规范的 o 最小扩展中 $\mathcal{米}$.