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Topology

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Finer Topologies on the Reals

TOPO-M9F9LB

Which of the following topologies on $\mathbb{R}$ are finer than the standard topology?

Select ALL that apply.

A

The collection of unions of sets of the form $[a,b)$, where $a,b\in\mathbb{R}$

B

$\{\emptyset, \mathbb{R}\}$

C

The collection of unions of sets of the form $B_\epsilon (x)=\{y\in\mathbb{R} : |x-y| < \epsilon\}$

D

$\mathcal{P}(\mathbb{R})$

E

$\{U\subseteq R : 0\in U$ or $U=\emptyset\}$