gn.general topology – Clopen base for topological space

Leave $ (X, d) $ a metric space, $ B (x, varepsilon): = {y in X | ~ d (x, y) < varepsilon } $ where $ x in X $ Y $ varepsilon> 0 $ Y $ (X, mathcal {T} _d) $ The natural topological space for the metric space. $ (X, d) $. Let's suppose $ B (x, varepsilon) $ It is closed for everyone $ x in X $ Y $ varepsilon> 0 $, so

$ 1. $ Every $ A in mathcal {T} _d $ Is it clopen?

$ 2. $ Yes $ A $ Is it closed then it can be written as a union of elements of the base?