论文标题
在$ p $ topary offiped封闭的字段中拓扑可解释的组
Topologizing interpretable groups in $p$-adically closed fields
论文作者
论文摘要
我们认为在$ p $ offile offiped offile offy office offient $ k $中的可解释的拓扑空间和拓扑组。我们确定具有拓扑驯服属性（如通用连续性）的特殊类别的“可允许拓扑”，类似于$ k^n $的可确定子集的拓扑。我们显示每一个可解释的集合都有至少一个可接受的拓扑结构，每个可解释的群体都有独特的可接受的群体拓扑。然后，我们考虑可解释的群体上可确定的紧凑性（在福纳西罗的意义上）。我们表明，当且仅当它具有有限令人满意的仿制药（FSG）时，可解释的组绝对紧凑，从而将早期结果推广到可确定的组上。结果，我们看到FSG是可解释组的可确定家庭中的可确定属性，并且在$ \ mathbb {q} _p $上定义的任何可解释的群体对一个可定义的组都具有同构。
We consider interpretable topological spaces and topological groups in a $p$-adically closed field $K$. We identify a special class of "admissible topologies" with topological tameness properties like generic continuity, similar to the topology on definable subsets of $K^n$. We show every interpretable set has at least one admissible topology, and every interpretable group has a unique admissible group topology. We then consider definable compactness (in the sense of Fornasiero) on interpretable groups. We show that an interpretable group is definably compact if and only if it has finitely satisfiable generics (fsg), generalizing an earlier result on definable groups. As a consequence, we see that fsg is a definable property in definable families of interpretable groups, and that any fsg interpretable group defined over $\mathbb{Q}_p$ is definably isomorphic to a definable group.
