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)
“Let us stop being afraid. Of our own thoughts, our own minds. Of madness, our own or others’. Stop being afraid of the mind itself, its astonishing functions and fandangos, its complications and simplifications, the wonderful operation of its machinery—more wonderful because it is not machinery at all or predictable.”
—Kate Millett (b. 1934)