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MacBookPro.lan 2025-6-2:19:39:55

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oskar
2025-06-02 19:39:55 +02:00
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application continue.md
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@@ -14,7 +14,7 @@ tags: "#s/maths/analyse"
> Soit $f: X \to Y$ une [[application]] > Soit $f: X \to Y$ une [[application]]
> Soit $a \in X$ > Soit $a \in X$
> On dit que $f$ est **continue en $a$** si : > On dit que $f$ est **continue en $a$** si :
> $\exists \varepsilon>0,\quad \exists \eta>0,\quad \forall x \in X,\quad d_{x}(x, a) < \eta \implies d_{y}(f(x), f(a)) < \varepsilon$ > $\forall \varepsilon>0,\quad \exists \eta>0,\quad \forall x \in X,\quad d_{x}(x, a) < \eta \implies d_{y}(f(x), f(a)) < \varepsilon$
^definition ^definition
- i On note $\mathcal{C}(E, F)$ l'[[ensemble des fonctions continues]] de $E \to F$ - i On note $\mathcal{C}(E, F)$ l'[[ensemble des fonctions continues]] de $E \to F$