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Topic: Disconnecting the plane.
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William Elliot

Posts: 2,637
Registered: 1/8/12
Disconnecting the plane.
Posted: Jun 26, 2013 1:20 AM
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Here's a toughie from Ask-a-Topologist.

Let L be a closed subspace of R^2 for which every point of L is a cut point.
Is R^2 - L disconnected. I think so.
How could it be proven (or disproved) that R^2 - I is disconnected?
Could this problem be related to the Jordan curve theorem?

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