# 离散 与 紧 Hausdorff　`prop.pontryagin-discrete-compact-duality`
Pontryagin 对偶把离散与紧互换
layer 18 · 命题 · 拓扑阿贝尔群 · 凝聚态数学+拓扑学
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设 $M$ 是局部紧 Hausdorff 阿贝尔群，$\widehat{M} = C_{\mathbb{Z}}(M, \mathbb{T})$ 是它的 Pontryagin 对偶。则
> 陈述续见 [nodes/prop.pontryagin-discrete-compact-duality.2.md](./prop.pontryagin-discrete-compact-duality.2.md)


## 为什么成立（入边，证明在 proofs/）
- …另有入边，续页见 [nodes/prop.pontryagin-discrete-compact-duality.3.md](./prop.pontryagin-discrete-compact-duality.3.md)

refs: Le Stum, §6.2；Le Stum, Exercise 6.9

> 说明见 `notes/prop.pontryagin-discrete-compact-duality.md`

引用：`prop.pontryagin-discrete-compact-duality`（内容 v0.9.0）· 条款见 [LICENSE.txt](../LICENSE.txt)