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# Bases For The Standard Topology On The Reals

TOPO-NYGT7K

Which of the following are bases for $\mathbb{R}$ endowed with the standard (metric) topology?

A

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

B

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

C

$\{\{a\} : a\in\mathbb{R}\}$

D

$\{[a,b] : a,b\in\mathbb{R}\}$

E

$\{B_\epsilon (x) : x\in\mathbb{R}^2, \epsilon\in\mathbb{R}\}$, where $B_\epsilon (x)$ is the ball in $\mathbb{R}^2$ of radius $\epsilon$ centered at $x$.