91Ó°ÊÓ

Give examples of incomplete metric spaces possessing complete subspaces.

Give examples to show that an infinite intersection of open sets may not be open, and an infinite union of closed sets may not be closed. [Hint: Show that $$ \bigcap_{n=1}^{\infty}\left(-\frac{1}{n}, \frac{1}{n}\right)=\\{0\\} $$ and $$ \left.\bigcup_{n=2}^{\infty}\left[\frac{1}{n}, 1-\frac{1}{n}\right]=(0,1) .\right] $$