Sunday, December 09, 2018

[jeuofkrj] Sphere with one point missing

A sphere (2-sphere) and a sphere with one point removed are topologically very different objects: the latter can be deformed to a disc or a plane.  What a difference a point makes!

Conversely, it also suggests that a plane plus one additional point ("a point at infinity") is "equivalent" to a sphere.  We see this in the stereographic map projection, which must omit one point.

Higher dimensions?

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