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Let $(X,\tau)$ be a topological space and let $\{U_i\}_{i\in \mathbb{N}}$ be an indexed family of open subsets in $\tau$.

Which of the following sets must also be open?

Select ALL that apply.

$\bigcup_{i\in \mathbb{N}} U_i$

$\bigcap_{i\in \mathbb{N}} U_i$

$\bigcup_{i\in\mathbb{N}} (U_i\cap U_{i+2})$

$\bigcap_{i\in\mathbb{N}} (X - U_i)$

$\emptyset\cup (U_3\cap U_7)$