Date: Feb 28, 2013 11:27 PM
Author: William Elliot
Subject: Michael construction

Let M be a subset of a normal space S. Define S_M as S given the 
base { U, {x} | U open within S, x in M } (Michael construction).

If in addition, S\M is normal, is S_M normal?

It's know that if M is open or if S is hereditarily normal, then S_M is 
normal.  (Normal is used without requiring Hausdorff.)