On relatively normal spaces
by
Jamal Tartir
Ohio University
Coauthors: M. V. Matveev, O. Pavlov

A subspace Y of X is relatively normal (strongly normal) in X if whenever E and F are disjoint closed in X (Y) subsets of X (Y), there are disjoint open subsets U and V of X such that E \cap Y subset or equal U and F \cap Y subset or equal V. For any regular (Tychonoff) space Y, the following are equivalent. (a) Y is either Lindelöf or nearly compact (b) Y is strongly normal in every larger regular (Tychonoff) space. (c) Y is normal in every larger regular (Tychonoff) space.

Date received: February 12, 1998