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