Set S=Q$\cap$(0,1) I wanted to show that this can not be expressed as intersection of countable collection of open sets.
I know Any closed set can be shown as intersection of countable collection of open set .
I had hint show this by Cantor intersection property which says that infinite intersection of nested sequence of nonempty compact set is nonempty . I could not able to link this hint with problem till now .Any help will be appreciated
Without using Baire Category Theorem Is it possible to solve this problem? As this problem occur in exercise where there in no mention of that theorem in text.