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sav08:tarski_s_fixpoint_theorem [2008/05/07 22:50] giuliano |
sav08:tarski_s_fixpoint_theorem [2009/03/26 10:36] vkuncak |
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**Lemma:** The value $a_*$ is a prefix point. | **Lemma:** The value $a_*$ is a prefix point. | ||
- | Observation: $a_*$ need not be a fixpoint. | + | Observation: $a_*$ need not be a fixpoint (example in exercises, e.g. on lattice [0,1] of real numbers). |
**Definition:** A function $G$ is $\omega$-continuous if for every chain $x_0 \sqsubseteq x_1 \sqsubseteq \ldots \sqsubseteq x_n \sqsubseteq \ldots$ we have | **Definition:** A function $G$ is $\omega$-continuous if for every chain $x_0 \sqsubseteq x_1 \sqsubseteq \ldots \sqsubseteq x_n \sqsubseteq \ldots$ we have |