Question: A Flatlander knows he lives on either a sphere or a projective plane. How can he tell which it is? A second Flatlander knows he

A Flatlander knows he lives on either a sphere or a projective plane. How can he tell which it is? A second Flatlander knows he lives on either a projective plane or a Klein bottle; how can he decide

Is protective three-space orientable? If you cross the boundary, how do you come back?

Is orientability a local or a global property? Is it topological or geometrical?

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