I read somewhere that a Geometry is a non Empty set and a subset of its power set which has subsets with at least two elements.The elements of the first set are called points and the elements of the second set are called lines.With specifying these two sets and considering some axioms,you will get a geometry.Now I have two questions.(adsbygoogle = window.adsbygoogle || []).push({});

1-As with vector spaces(which you can define things as vectors too different from arrows in space),Can I build a geomery with e.g. the set of all 2x2 matrices?

2-What is the relationship of this approach to geometry with the manifold geometry?

thanks

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# Different approches to Geometry

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