# gn.general topology – Example of a compact \$alpha\$-normal space which is not normal

Could you help me to find an example of a compact space which is $$alpha$$-normal, but not normal? The definition of $$alpha$$-normal is any disjoint closed subsets $$A, B$$ can be separated by disjoint open subsets $$U, V$$ such that $$Ucap A$$ is dense in $$A$$ and $$Vcap B$$ is dense in $$B$$.

Thank you.