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We have $K = \{\frac 1n: n=1,2,3,\ldots\}$. The set $B$ is a collection of subsets of $\mathbb{R}$. Precisely, the elements of $B$ are all of the intervals $(a,b)$, together with the sets $$(a,b)\setminus K = \{x\in\mathbb{R}: a\leq x\leq b \mbox{ and } x\neq \frac 1n \forall n\geq 1\}.$$ So, for example, the interval $(-3,1)$ is an element of $B$. So is the set $(5,10)\setminus K$.

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