I'm having some trouble with the following questions:

Let $S$ be any set and $\epsilon$ > 0. Define $T$ = {$t$ $\in$ $\mathbb{R}$ : |$t - s$| < $\epsilon$ for some $s \in S$}. Prove that T is open. 

Now, again let $S$ be any set and define $V$ = {$t$ $\in$ $\mathbb{R}$ : |$t - s$| $\le$ 1 for some $s \in S$}. Is $V$ necessarily closed?

Thanks you for any help you can provide!