# 凝聚态集满态射的判据　`prop.cond-epi`
凝聚态集的满态射
layer 17 · 命题 · 凝聚态集 · 凝聚态数学
[在星图里打开](../#n=prop.cond-epi)　·　[节点索引](../index.md)

凝聚态集的态射 $X \to Y$ 是满态射 $\iff$ 对每个**自由**紧 Hausdorff 空间 $F$，$X(F) \to Y(F)$ 是满射。

## 为什么成立（入边，证明在 proofs/）
- [`def.sheaf`](../nodes/def.sheaf.md) 层 + [`prop.cond-projectives`](../nodes/prop.cond-projectives.md) Cond 有足够多投射对象 + [`def.free-presentation`](../nodes/def.free-presentation.md) 自由表示：满态射在自由空间上逐点检验　[proofs/imp.cond-epi.md](../proofs/imp.cond-epi.md)
- [`def.sheaf`](../nodes/def.sheaf.md) 层：用到了定义 层　[proofs/def-dep.sheaf-cond-epi.md](../proofs/def-dep.sheaf-cond-epi.md)

- …另有入边，续页见 [nodes/prop.cond-epi.2.md](./prop.cond-epi.2.md)

## 它能推出什么 / 谁在用它
- …另有出边，续页见 [nodes/prop.cond-epi.3.md](./prop.cond-epi.3.md)

refs: Le Stum, An introduction to condensed mathematics, §4

引用：`prop.cond-epi`（内容 v0.9.0）· 条款见 [LICENSE.txt](../LICENSE.txt)