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)
“Though there were numerous vessels at this great distance in the horizon on every side, yet the vast spaces between them, like the spaces between the stars,—far as they were distant from us, so were they from one another,—nay, some were twice as far from each other as from us,—impressed us with a sense of the immensity of the ocean, the “unfruitful ocean,” as it has been called, and we could see what proportion man and his works bear to the globe.”
—Henry David Thoreau (1817–1862)