Normal space and Tietze/Urysohn

I’m having a really hard time with this one. On a conceptual level and on a technical level. I’ve got my three topology books here, but I can’t seem to make anything out of it. Can somebody enlighten me?

Let be a topological space. And let be normal and a countable family of closed subsets of . Suppose that every point of has an neighbourhood such that for at most one . (Note in perticular that when .)

Prove: there are open sets such that for each and such that when

(Use Tietze Extension Theorem or Urysohn’s lemma)