# 底空间保有限积　`cor.cond-ktop-finite-products`
推论：$(X \times Y)(\cdot) \;\cong\; k\bigl(X(\cdot) \times Y(\cdot)\bigr)$
layer 18 · 推论 · 凝聚态集 · 凝聚态数学
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函子 $\mathrm{Cond} \to k\mathbf{Top}$，$X \mapsto X(\cdot)$，**保有限积**：对任意 $X, Y \in \mathrm{Cond}$，

$$(X \times Y)(\cdot) \;\cong\; k\bigl(X(\cdot) \times Y(\cdot)\bigr).$$
> 陈述续见 [nodes/cor.cond-ktop-finite-products.2.md](./cor.cond-ktop-finite-products.2.md)


## 为什么成立（入边，证明在 proofs/）
- …另有入边，续页见 [nodes/cor.cond-ktop-finite-products.3.md](./cor.cond-ktop-finite-products.3.md)

## 它能推出什么 / 谁在用它
- …另有出边，续页见 [nodes/cor.cond-ktop-finite-products.4.md](./cor.cond-ktop-finite-products.4.md)

refs: Le Stum, An introduction to condensed mathematics, Corollary 4.2.7

> 说明见 `notes/cor.cond-ktop-finite-products.md`

引用：`cor.cond-ktop-finite-products`（内容 v0.9.0）· 条款见 [LICENSE.txt](../LICENSE.txt)