I'm looking for an example of a domain(continuos dcpo) which isn't an L-domain(every principal ideal is a complete lattice)
2025-01-13 02:41:10.1736736070
Domain not L-domain
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How about this one:
The principal ideal $\mathord\downarrow \{a\}$ is not a complete lattice, as the subset $\{d,e\}$ has no supremum. It is a dcpo, since any directed set that does not contain $a$ must also not contain $b$ or not contain $c$.