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Three counterexamples concerning ω-chain completeness and fixed point properties

1981
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Proceedings of the Edinburgh Mathematical Society
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A partially ordered set, is -chain, in P, the least upper bound of C, denoted by sup C, exists. Notice that C could be empty, so an o> -chain complete partially ordered set has a least element, denoted by 0. A function / mapping a partially ordered set P into a partially ordered set Q is chain continuous if for any nonempty chain C in P, which has a supremum, /(sup P C) = sup Q /(C). It is o>-chain continuous if for any nonempty countable chain C in P, which has a supremum, /(sup P C) = sup Q

doi:10.1017/s0013091500006453
fatcat:dl6evteftnbetjpk67lqubc34u