# Failure of Baire Category Theorem if collection of sets is not closed or not countable.

The Baire Category Theorem implies that $\mathbb{R}^n$ cannot be written as the union of a countable collection of closed subsets having empty interior.

I was wondering how it can be showed that this fails if the sets are not specified to be closed, or the collection is not required to be countable.

Help is appreciated. Thanks