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eduroam-prg-sg-1-45-234.net.univ-paris-diderot.fr 2025-9-23:14:30:53

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suite convergente.md
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@@ -12,8 +12,8 @@ tags: "#s/maths/analyse"
> $\forall \varepsilon >0, \quad \exists n_0 \in N, \quad \forall n \geq n_0, \quad d(u_{n}, l) < \varepsilon$
^definition
> [!definition] [[suite convergente]] dans un [[espace topologique]]
> Soit $(E, \mathscr{T})$ un [[espace topologique]]
> [!definition] [[suite convergente]] dans un [[structure de topologie]]
> Soit $(E, \mathscr{T})$ un [[structure de topologie]]
> Soit $(u_{n}) \in E^{\mathbb{N}}$
> $(u_{n})$ **converge vers** $l \in E$ $\iff$ $\forall V \in \mathcal{V}(l),\quad \exists N \in \mathbb{N},\quad \forall n \geq N,\quad u_{n} \in V$
>