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Update Math4201_L2.md

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Zheyuan Wu
2025-09-06 18:15:00 -05:00
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@@ -16,7 +16,7 @@ A topological space is a pair of set $X$ and a collection of subsets of $X$, den
2. $\mathcal{T}$ is closed with respect to arbitrary unions. This means, for any collection of open sets $\{U_\alpha\}_{\alpha \in I}$, we have $\bigcup_{\alpha \in I} U_\alpha \in \mathcal{T}$ 2. $\mathcal{T}$ is closed with respect to arbitrary unions. This means, for any collection of open sets $\{U_\alpha\}_{\alpha \in I}$, we have $\bigcup_{\alpha \in I} U_\alpha \in \mathcal{T}$
3. $\mathcal{T}$ is closed with respect to finite intersections. This means, for any finite collection of open sets $\{U_1, U_2, \ldots, U_n\}$, we have $\bigcap_{i=1}^n U_i \in \mathcal{T}$ 3. $\mathcal{T}$ is closed with respect to finite intersections. This means, for any finite collection of open sets $\{U_1, U_2, \ldots, U_n\}$, we have $\bigcap_{i=1}^n U_i \in \mathcal{T}$
The elements of $\mathcal{T}$ are called open sets. The elements of $\mathcal{T}$ are called **open sets**.
The topological space is denoted by $(X, \mathcal{T})$. The topological space is denoted by $(X, \mathcal{T})$.