Homogeneous Spaces
In other words, the "traditional spaces" are homogeneous spaces; but not for a uniquely determined group. Changing the group changes the appropriate geometric language.
In today's language, the groups concerned in classical geometry are all very well known as Lie groups: the classical groups. The specific relationships are quite simply described, using technical language.
Read more about this topic: Erlangen Program
Famous quotes containing the words homogeneous and/or spaces:
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—William Faulkner (1897–1962)
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—Joyce Carol Oates (b. 1938)