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:
“Your notions of friendship are new to me; I believe every man is born with his quantum, and he cannot give to one without robbing another. I very well know to whom I would give the first place in my friendship, but they are not in the way, I am condemned to another scene, and therefore I distribute it in pennyworths to those about me, and who displease me least, and should do the same to my fellow prisoners if I were condemned to a jail.”
—Jonathan Swift (1667–1745)
“One who shows signs of mental aberration is, inevitably, perhaps, but cruelly, shut off from familiar, thoughtless intercourse, partly excommunicated; his isolation is unwittingly proclaimed to him on every countenance by curiosity, indifference, aversion, or pity, and in so far as he is human enough to need free and equal communication and feel the lack of it, he suffers pain and loss of a kind and degree which others can only faintly imagine, and for the most part ignore.”
—Charles Horton Cooley (1864–1929)