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The real projective plane is not simply connected

Ciro Santilli (@cirosantilli, 37) ... Mathematics Area of mathematics Geometry Projective geometry Real projective space Real projective plane
Updated 2025-07-16  0 By others on same topic  0 Discussions Create my own version
To see that the real projective plane is not simply connected space, considering the lines through origin model of the real projective plane, take a loop that starts at (1,0,0) and moves along the y=0 great circle ends at (−1,0,0).
Note that both of those points are the same, so we have a loop.
Now try to shrink it to a point.
There's just no way!

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