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Topology

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Clopen Sets In Topologies On The Reals 1

TOPO-7K74Q4

Let $\tau=\{U\subseteq \mathbb{R} : \mathbb{R} - U$ is finite or $U=\emptyset\}$. Then $\tau$ is a topology on $\mathbb{R}$. Which of the following subsets of $\mathbb{R}$ is neither open nor closed in this topolgy?

A

$\{-1,2,7,19\}$

B

$\{x\in\mathbb{R} : x^3+x^2\neq 2x\}$

C

$\mathbb{Q}$

D

$\{x\in\mathbb{R} : x^2=1\}$

E

$\{x\in\mathbb{R} : x\neq 0\}$