Each elliptic space can be modelled with a real projective space. The best thing is to just start thinking about the real projective plane.
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Non-Euclidean geometry refers to any form of geometry that is based on axioms or postulates that differ from those of Euclidean geometry, which is the geometry of flat surfaces as described by the ancient Greek mathematician Euclid. The most notable feature of Non-Euclidean geometry is its treatment of parallel lines and the nature of space.