MacBook-Pro-de-Oscar.local 2026-1-19:19:25:53

This commit is contained in:
oskar
2026-01-19 19:25:53 +01:00
parent ed1f8dbcb3
commit 15d5a5f442
9 changed files with 65 additions and 449 deletions

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@@ -1,6 +1,6 @@
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==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
# Text Elements
# Excalidraw Data
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g ( h ⍵) ^fceSJhCG
%%
# Drawing
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## Drawing
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```
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@@ -43,4 +43,3 @@ tags: "#s/obsidian"

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@@ -69,6 +69,8 @@ tags: "#s/maths/algèbre"
> > Donc $V$ est ouverte
^intersection-ouverts
> [!proposition]+ Ouvert d'une partie
> Soit $(X, d)$ un [[espace métrique]]
> Soit $(Y, d) \subset (X, d)$
@@ -100,6 +102,7 @@ tags: "#s/maths/algèbre"
> $\begin{align} B(x, 1-x) &= \{ y\in\mathbb{R}\mid |y-x| < 1-x \}\\&= \{ y \in \mathbb{R}| x-1 < y-x < 1-x \}\\&= \left\{ y\in\mathbb{R}\mid \underbracket{2x-1}_{>0 \text{ si } x > \frac{1}{2}} < y < 1 \right\} \\&= \subset ]0; 1[ \end{align}$
> [!example] $[0; 1[$ n'est pas un ouvert de $\mathbb{R}$
> en effet, on a, pour tout $r > 0$ :
> $\begin{align} B(0, r) &= \{ y \in \mathbb{R}\mid d(y, 0) < r \}\\&= \{ y\in\mathbb{R}\mid |y|<r \}\\&= \{ y\in\mathbb{R}\mid -r<y<r \} \end{align}$