Counter Example for the union of any number of compact sets is compact in T2-spaces

Question

We know that, the intersection of arbitrary many compact sets is compact in Hausdorff Spaces.

I need counter example analogous of above proposition for the union is not true. When I consider, logically it does not have to be compact but I cannot find a counter example in one way or another. Could someone give a counter example please? Thanks

Answer 1

Just consider the union of all the singletons in $\mathbb{R}$.