I've been thinking about the proof. Although it seems very obvious that by the definition of $F_\sigma$ sets, a set is an $F_\sigma$ set if it is a countable union of closed sets, so intuitively, a single closed set is also a collection of '1' closed sets.... But this seems to be a little trivial, it might be that this is actually correct but i am really confused.
Another doubt that came to my mind is whether:' closed set of real numbers' means a collection of singletons?, if yes then would it be different from an 'open set of real numbers'? what is a 'closed set composed of in ANY topological space'? Really new to the subject, trying to get the feel for it..