fixed points of normal functions

If f:M𝐎𝐧 is a function from any set of ordinalsMathworldPlanetmathPlanetmath to the class of ordinals then Fix(f)={xMf(x)=x} is the set of fixed points of f. f, the derivativeMathworldPlanetmath of f, is the enumerating function of Fix(f).

If f is κ-normal ( then Fix(f) is κ-closed and κ-normal, and therefore f is also κ-normal.

For example, the function which takes an ordinal α to the ordinal 1+α has a fixed point at every ordinal ω, so f(α)=ω+α.

Title fixed points of normal functions
Canonical name FixedPointsOfNormalFunctions
Date of creation 2013-03-22 13:28:59
Last modified on 2013-03-22 13:28:59
Owner Henry (455)
Last modified by Henry (455)
Numerical id 6
Author Henry (455)
Entry type Definition
Classification msc 03E10
Related topic ProofOfPowerRule
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Related topic DirectionalDerivative
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Defines derivative