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Topology

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Open Covers and Finite Subcovers

TOPO-KDBVX8

Which of the following open covers of $\mathbb R$ has a finite subcover?

A

$\{U_n:n\in\mathbb Z\}$ where $U_n=(n-1,n+1)$

B

$\{U_n:n\in\mathbb N\}$ where $U_n=(-n,n)$

C

$\{U_n:n\in\mathbb N\}$ where $U_n=\bigcup_{k=-\infty}^{\infty}(10k-n, 10k+n)$

D

$\{U_n:n\in\mathbb N\}$ where $U_n=(-\infty,n)$