\text { 1. Let } X \text { be a metric space, and let } U \text { and } V \text { be connected subsets of } X \text

{. Is } U \cap V \text { connected? Prove it, or give a } counterexample. \text { 2. Let } C_{n} \subseteq \mathbb{R}^{2}, n=1,2, \ldots \text { be an infinite collection of closed connected subsets such that } C_{1} \geq C_{2} \supseteq C_{3} \supseteq \ldots \text { Is the intersection } \bigcap_{n \geq 1} C_{n} \text { connected? Prove it, or give a counterexample. }