Algebra of Functions
The algebra of continuous (real or complex) functions on a Hausdorff space is a commutative C*-algebra, and conversely by the Banach–Stone theorem one can recover the topology of the space from the algebraic properties of its algebra of continuous functions. This leads to noncommutative geometry, where one considers noncommutative C*-algebras as representing algebras of functions on a noncommutative space.
Read more about this topic: Hausdorff Space
Famous quotes containing the words algebra of, algebra and/or functions:
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (1883–1955)
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (1883–1955)
“The mind is a finer body, and resumes its functions of feeding, digesting, absorbing, excluding, and generating, in a new and ethereal element. Here, in the brain, is all the process of alimentation repeated, in the acquiring, comparing, digesting, and assimilating of experience. Here again is the mystery of generation repeated.”
—Ralph Waldo Emerson (1803–1882)