Structures of Geometry
The objects of modern Geometry, spaces, like all objects of modern Mathematics, are sets of elements of arbitrary nature endowed with some mathematical structure. Such is the formulation in the best Encyclopaedia of Mathematics, the Elements of Mathematics by N. Bourbaki [Boul–9]. Many books in this encyclopaedic series, in particular Topological Vector Spaces [Bou5], and Lie Groups and Algebras [Bou8], are closely connected with modern Geometry, and the title Elements of Bourbaki emphasizes that this mathematical Encyclopaedia is a successor of the classical mathematical Encyclopaedia of Antiquity, the Elements of Euclid [Euc], the main part of which is devoted to geometry.
KeywordsTopological Space Symmetric Space Homogeneous Space Natural Topology Invariant Subgroup
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