If anyone helps me with these questions, I will be thankful.

(a) Show that every closed set in a metric space can be expressed as an

intersection of countably many open sets.

(b) Show that every open set in a metric space can be expressed as an

union of countably many closed sets. (Hint: take complements.)

(c) Express the interval (0, 1) in R as a union of countably many open

sets.