A. A non empty countable set cannot be open.
B. For a non empty set the uncountable is necessary condition for that set to be open.
C. Uncountability is a sufficient condition for a set to be open.
D. A closed set can be uncountable or countable.
My effort: If i suppose an open set (0,1) with elements belonging to Set of rational numbers, then the set (0,1) will be countable.So there do exist an open interval which is countable.Right?
for option D, The closed set [0,1] is countable in Q but not in R.hence, i say that a closed set can be both countable and uncountable.
This is a multiple select question.