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Diffstat (limited to 'mindmap/limit.org')
| -rw-r--r-- | mindmap/limit.org | 2 |
1 files changed, 1 insertions, 1 deletions
diff --git a/mindmap/limit.org b/mindmap/limit.org index e8ef2ea..d90eabf 100644 --- a/mindmap/limit.org +++ b/mindmap/limit.org @@ -95,7 +95,7 @@ in every neighbourhood of some $x \in X$, and thus converges. #+end_proof and finally we get the Bolzano-Weierstrass theorem for $\mathbb{R}^{n}$ for free, as $\mathbb{R}^{n} \cup \lbrace \infty\rbrace$ is a compact metric space: #+begin_corollary -Every sequence in $R^{n}$ either has a convergent subsequence, or has a subsequence that escapes to $\infty$. +Every sequence in $\mathbb{R}^{n}$ either has a convergent subsequence, or has a subsequence that escapes to $\infty$. #+end_corollary Also, for the two-point compactification, it yields this result as well if you're working in that space: #+begin_corollary |