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Topology

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Moderate

Bases For The Discrete Topology

TOPO-XMZ21J

Consider the topological space $(\mathbb{C}, \tau)$, where $\tau$ is the discrete topology on $\mathbb{C}$.

Which the following are bases for this topology?

A

$\{(a,b) : a,b\in\mathbb{R}\}$

B

$\{(a,b) : a,b\in\mathbb{C}\}$

C

$\{\emptyset, \mathbb{C}\}$

D

$\{\{z\} : z\in\mathbb{C}\}\cup\{\emptyset\}$

E

$\{\{z,w\} : z, w\in\mathbb{C}\}\cup\{\emptyset\}$