A locally compact group G is said to be approximable by totally disconnected subgroups if there is a sequence of closed totally disconnected subgroups \((\Gamma _n)_{n\in {\mathbb N}}\) of G such that for any non-empty open set O of G, there exists an integer k such that \(O\cap \Gamma _n \ne \varnothing \), for every \(n\ge k\). In this paper, we prove that every pro-torus is approximable by profinite subgroups and we provide a characterization of the approximation of compact groups. Furthermore, we show that every compactly generated locally compact abelian group is approximable by totally disconnected subgroups. As an application, a study of the Chabauty space of closed totally disconnected subgroups is given.

甲局部紧组ģ被说成是由完全断开子组可近似是否有关闭完全断开子组的一个序列\（（\伽玛_n）_ {N \在{\ mathbb N}} \）的G ^，使得对于任何非空开集ø的ģ，存在一个整数ķ使得\（O \帽\伽玛_n \ NE \ varnothing \） ，对于每一个\（N \锗的K \）。在本文中，我们证明了每个protorus都可以由有限子群逼近，并且我们提供了紧群的逼近的一个特征。此外，我们表明，每个紧密生成的局部紧致阿贝尔群都可以通过完全断开的子群近似。作为一种应用，研究了封闭的完全不连接的子群的Chabauty空间。