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Joined: Mon Nov 09, 2015 1:36 am Posts: 460 Location: Ioannina, Greece

 Give an example of a descending sequence $(F_n)_{n\in\mathbb{N}}$ of nonempty closed subsets of metric space $(\mathbb{R}, \cdot)$, such that $\bigcap_{n=1}^{\infty}F_n=\varnothing$.
 Give an example of a descending sequence $(F_n)_{n\in\mathbb{N}}$ of nonempty closed subsets of metric space $(\mathbb{Q}, \cdot)$, such that ${\rm{diam}}(F_n)\xrightarrow{n\to+\infty} 0$ and $\bigcap_{n=1}^{\infty}F_n=\varnothing$.
_________________ Grigorios Kostakos

