Dipartimento di Matematica, Citta Universitaria, Viale A.Doria 6, 95125, Catania, Italy ; Moscow Center for Continuous Mathematical Education, B.Vlas'evskij per. 11, 121002, Moscow, Russia
Abstract:
It is proved that a Tychonoff space is Lindelöf if and only if whenever a Tychonoff space contains two disjoint closed copies and of , then these copies can be separated in by open sets. We also show that a Tychonoff space is weakly -embedded (relatively normal) in every larger Tychonoff space if and only if is either almost compact or Lindelöf (normal almost compact or Lindelöf).