A is non empty set of R and set of interior points of A is empty. Then A is countable at most.
How to (dis)prove it?
Empty interior for non-empty set implies that A consist of isolated points. I cannot imagine uncountable (i.e. infinite) set of isolated points, that's why I tend to think that the statement is true. Could you help me to prove?
Best Answer
take all non-rationals. there's uncountably many of them yet their interior is empty