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Let $X=\{0,1,2\}$. Which of the following form a basis for some topology on $X$?

Select ALL that apply.

A

$\{\emptyset,\{0\},\{1\},\{2\}\}$

B

$\{ \emptyset, \{ 0 \}, \{ 1 \} \}$

C

$\mathcal{P}(X)$

D

$\{\emptyset, \{0\}, \{0,1\}, \{0,2\}\}$

E

$\{\{1,2\}\}$

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