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Topic: Nowhere Dense
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William Elliot

Posts: 248
Registered: 10/7/08
Nowhere Dense
Posted: Jun 30, 2011 9:30 AM
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If A\B is nowhere dense, then int cl A subset cl B.

The converse doesn't hold; for example, A = Q, B = R\Q.

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If int cl A subset cl int B, then A\B is nowhere dense.

The converse doesn't hold; for example, A = B = (0,1) /\ Q.

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It there some similar property for A and B
that's equivalent to A\B is nowhere dense?

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