fix typo and formatting errors

This commit is contained in:
Zheyuan Wu
2025-10-09 21:37:22 -05:00
parent 9734128293
commit f9c5889564
7 changed files with 130 additions and 25 deletions

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@@ -20,7 +20,9 @@ The elements of $\mathcal{T}$ are called **open sets**.
The topological space is denoted by $(X, \mathcal{T})$.
#### Examples
<details>
<summary>Examples of topological spaces</summary>
Trivial topology: Let $X$ be arbitrary. The trivial topology is $\mathcal{T}_0 = \{\emptyset, X\}$
@@ -40,12 +42,18 @@ $\mathcal{T}_2 = \{\emptyset, \{a\}, \{a,b\}\}$
$\mathcal{T}_3 = \{\emptyset, \{b\}, \{a,b\}\}$
Non-examples:
</details>
<details>
<summary>Non-example of topological space</summary>
Let $X=\{a,b,c\}$
The set $\mathcal{T}_1=\{\emptyset, \{a\}, \{b\}, \{a,b,c\}\}$ is not a topology because it is not closed under union $\{a\} \cup \{b\} = \{a,b\} \notin \mathcal{T}_1$
</details>
#### Definition of Complement finite topology
Let $X$ be arbitrary. The complement finite topology is $\mathcal{T}\coloneqq \{U\subseteq X|X\setminus U \text{ is finite}\}\cup \{\emptyset\}$