From 8bebbe584cf4fe03bef488d5d50c724e690e7c73 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Mon, 27 Oct 2025 11:22:06 +0100 Subject: [PATCH] [Analysis] Notes from exercise session --- .../analysis-ii/analysis-ii-cheat-sheet.pdf | Bin 280596 -> 280596 bytes .../vectors/differentiation/00_continuity.tex | 1 + 2 files changed, 1 insertion(+) diff --git a/semester3/analysis-ii/analysis-ii-cheat-sheet.pdf b/semester3/analysis-ii/analysis-ii-cheat-sheet.pdf index a24de26f57af6ec76eb75c7ccc3db5512de17381..368ef21b05e8ce1f7f9640a6516629cf0fb323a8 100644 GIT binary patch delta 146 zcmbO-L2$|h!G;#b7N!>FEiCUHH4P0+jExMm4Gh%{4AeEb^nLSFToOxC6*OF|j0}uS z4GoOUAxgGOII)y7xf;8eIU2b-IU6}yn3x;8IGVXx8ksmbJ6V_+n>iU78rdn>5L6O7 PedB*-)9swDEZoch)i)%i delta 146 zcmbO-L2$|h!G;#b7N!>FEiCUHH4V&7jf^d{4Gh%{4AeEb^nLSFToOxC6*OF|j0}uS z4GoOUAxgGOII)y7xmp^Snmf9-E diff --git a/semester3/analysis-ii/parts/vectors/differentiation/00_continuity.tex b/semester3/analysis-ii/parts/vectors/differentiation/00_continuity.tex index c2c177f..0e5b451 100644 --- a/semester3/analysis-ii/parts/vectors/differentiation/00_continuity.tex +++ b/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 % ──────────────────────────────────────────────────────────────────── \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\\ % ──────────────────────────────────────────────────────────────────── \shortex \bi{(1)} $\emptyset$ and $\R^n$ are closed.