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[Analysis] Small notes

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RobinB27
2026-01-26 14:58:58 +01:00
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semester3/analysis-ii/cheat-sheet-rb/parts/04_cont.tex
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@@ -119,7 +119,8 @@ $$\bigl\{ y \in \R^n \sep |x_i - y_i| < \delta,\ \ \forall i \leq n \bigr\} \su
$$
f^{-1}(Y) = \bigl\{ x \in \R^n \sep f(x) \in Y \bigr\} \text{ is closed/open.}
$$
\subtext{$f: \R^n \to \R^m$ is continuous,$\quad Y \subset \R^m$}
\subtext{$f: \R^n \to \R^m$ is continuous,$\quad Y \subset \R^m$}\\
\subtext{Note: $X$ open/closed, does \textit{not} imply $f(X)$ open/closed}
\lemma \textbf{The complement of open sets is closed}
$$