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:
“If we Americans are to survive it will have to be because we choose and elect and defend to be first of all Americans; to present to the world one homogeneous and unbroken front, whether of white Americans or black ones or purple or blue or green.... If we in America have reached that point in our desperate culture when we must murder children, no matter for what reason or what color, we don’t deserve to survive, and probably won’t.”
—William Faulkner (1897–1962)
“through the spaces of the dark
Midnight shakes the memory
As a madman shakes a dead geranium.”
—T.S. (Thomas Stearns)