cfα=β and αξ:ξ<β be cofinal in α, and

cfβ=γ and ξ(ν):ν<γ be cofinal in β.

The claim of the theorem cf(cfα)=cfα means that γ=β; we prove this fact.

Suppose γβ. Then γ<β by cfδδ.

Now, αξ(ν):ν<γ is seen to be confinal in α, which means that cfα=γ<β, a contradictionMathworldPlanetmathPlanetmath. Therefore, γ=β.

Title cf(cfα)=cfα
Canonical name operatornamecfoperatornamecfalphaoperatornamecfalpha
Date of creation 2013-03-22 18:11:22
Last modified on 2013-03-22 18:11:22
Owner yesitis (13730)
Last modified by yesitis (13730)
Numerical id 8
Author yesitis (13730)
Entry type Proof
Classification msc 03E04