Fixed point theorems on chain complete partially ordered sets (Q1849323)

The authors show that for posets the general fixed point property is equivalent to the fixed apex property. They also prove that for posets the locally general fixed point property is equivalent to the locally fixed apex property. Their main result is that a poset with the locally general fixed point property is chain complete. They prove that for lattices the general fixed point property is equivalent to the lattice being inductive. They provide counterexamples to some assertions of \textit{M. R. Tasković} [``Characterizations of inductive posets with applications'', Proc. Am. Math. Soc. 104, 650-659 (1988; Zbl 0689.05008)].