Other Notions of Degree
Similar notions of reduction and degree arise by replacing the continuous functions by any class of functions F which contains the identity function and is closed under composition. Write ≤F if for some function in F. Any such class of functions again determines a preorder on the subsets of Baire space. Degrees given by Lipschitz functions are called Lipschitz degrees, and degrees from Borel functions Borel-Wadge degrees.
Read more about this topic: Wadge Hierarchy
Famous quotes containing the words notions and/or degree:
“The idea of the sacred is quite simply one of the most conservative notions in any culture, because it seeks to turn other ideas—uncertainty, progress, change—into crimes.”
—Salman Rushdie (b. 1947)
“It would be difficult to exaggerate the degree to which we are influenced by those we influence.”
—Eric Hoffer (1902–1983)