# alpha stable

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• Jul 12th 2009, 05:09 PM
Sampras
alpha stable
Suppose $\alpha: X \times X \to X$. A subset $A \subseteq X$ is called $\alpha$-stable if and only if $x,y \in A \Rightarrow \alpha(x,y) \in A$.

What is the point of considering $\psi_{\alpha}(\psi_{\alpha}(A)) = \psi_{\alpha}(A)$? Is there any significance?
• Jul 16th 2009, 11:12 AM
Moo
Hello,

What is $\psi_\alpha$ ?