Motivation:
We know that every open set is a countable union of open intervals with rational endpoints and that every open interval is a countable union of closed intervals. Hence every open set is a countable union of closed intervals. It follows by De Morgan's laws that every closed set is a countable intersection of open sets.
I would like to ask if we can prove a stronger result that
every closed set is a countable intersection of open intervals.
Thank you for your help!