[Analysis] Notes from exercise session

semester3/analysis-ii/parts/vectors/differentiation/00_continuity.tex

@@ -47,6 +47,7 @@ $\Rightarrow f = (f_1, f_2): \R^n \rightarrow \R^{m_1 + m_2}$ is continuous (Car
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 \shortdef \bi{(1)} $X \subseteq \R^n$ is \bi{bounded} if the set of $||x||$ for $x \in X$ is bounded in $\R$
 \bi{(2)} $X \subseteq \R^n$ is \bi{closed} if $\forall (x_k)$ in $X$ that converge in $\R^n$ to some vector $y \in \R^n$, we have $y \in X$
+% Closed simple explanation: "border" included or not (and is not in case of open disc because limit is outside, i.e. limit of a_n = (n / (n + 1), 0) is 1)
 \bi{(3)} $X \subseteq \R^n$ is \bi{compact} if it is bounded and closed\\
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 \shortex \bi{(1)} $\emptyset$ and $\R^n$ are closed.