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Topic: Michael construction
Replies: 2   Last Post: Mar 2, 2013 4:01 AM

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William Elliot

Posts: 2,637
Registered: 1/8/12
Michael construction
Posted: Feb 28, 2013 11:27 PM
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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.)

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