Subconvergence (部分収束 / 部分空間) (Definition IV.3.11)

• Subconvergence (部分収束 / 部分空間) (Definition IV.3.11) #Card
  • For $V \subset X$ and the natural injection $j_V : V \to X$, the initial convergence $j_V^-\xi$ is called a subconvergence (or subspace) of $\xi$.

Back

Let $\xi$ be a convergence on $X$ and $V \subset X$. The initial convergence $j_V^-\xi$（$j_V : V \to X$, $j_V(x) := x$ は natural injection）is called a subconvergence or a subspace of $\xi$.

• $j_V^-\xi \approx \xi|V$（制限と同相）: $\lim{\xi|V} \mathcal{F} = V \cap \lim\xi \mathcal{F}$——第III章のcards/topology/restriction-of-a-convergenceが始収束の言葉で回収される。

Lean

部分空間位相 instTopologicalSpaceSubtype = induced Subtype.val