A closed curve on a sphere with a point not on the curve can be contracted to a point without crossing the point not the curve no matter where that point is.

Brent

On 1/24/2020 5:38 PM, Alan Grayson wrote:
Both are connected. Both have no boundary. Both are closed, since both contain their accumulation points. Both have uncountable elements. So how can they be distinguished within the context of point-set topology? TIA, AG
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