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Topic: Compactification
Replies: 15   Last Post: Mar 17, 2013 6:11 AM

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David Hartley

Posts: 463
Registered: 12/13/04
Re: Compactification
Posted: Dec 15, 2012 10:46 AM
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In message
Butch Malahide <> writes
>Here, if I'm not mistaken, is an example of a compact space K (a
>subspace of the complex plane) with two dense subspaces X and X' such
>that X is homeomorphic to X' while K\X is not homeomorphic to K\X'.
>K = {z: |z+2| <= 1 OR |z| <= 1 OR |z-2| <= 1}.
>A = {z: |z+2| < 1}, B = {z: |z| < 1}, C = {z: |z-2| < 1}.
>A_0 is a countable dense subset of A, B_0 is a countable dense subset
>of B, C_0 is a countable dense subset of C.
>X is the union of A, B_0, and C_0;
>X' is the union of A_0, B, and C_0.


I thought it should be possible but couldn't come up with an example

David Hartley

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