update notations and fix typos

This commit is contained in:
Zheyuan Wu
2025-02-25 20:41:35 -06:00
parent 419ea07352
commit 27bff83685
71 changed files with 920 additions and 430 deletions

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@@ -37,7 +37,7 @@ Let $h>0$. Since $y-h$ is not an upper bound of $E$, $\exists x\in E$ such that
Since $y$ is an upper bound of $E$, $x\leq y$. So $x\in B_n(y)\cap E$, so $B_h(y)\cap E\neq \phi$.
EOP
QED
#### Remark 2.29
@@ -75,7 +75,7 @@ To show $G\cap Y\subset E$.
$G\cap Y=\left(\bigcup_{p\in E}V_p\right)\cap Y=\bigcup_{p\in E}(V_p\cap Y)\subset E$
EOP
QED
### Compact sets
@@ -101,4 +101,4 @@ as we can build an infinite open cover $\bigcup_{i\in Z} (i,i+2)$ and it does no
Suppose we consider the sub-collection $\{n_i,n_i+2:i=1,..,k\}$, Then $N+3$ is not in the union, where $N=max\{n_1,...,n_k\}$.
EOP
QED