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Topic: Baire Example
Replies: 6   Last Post: Aug 21, 2014 12:25 AM

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William Elliot

Posts: 2,383
Registered: 1/8/12
Baire Example
Posted: Aug 18, 2014 2:30 AM
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Let A subset S, be a Baire subspace.
Is cl A a Baire subspace? No.

Within S = N \/ {p} with the topology { A, S | A subset N },
N is a Baire subspace and S = cl N isn't.

S is T0 and not T1. Is there a T1 or Hausdorff counter example?

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