Abstract. We prove that if the finite ordered sets P and X have the fixed point property then so too does P x X.Mathematics Subject Classification (1991). 06A06.
We discuss [2] of the same title and offer an alternative example. This example is a subalgebra of the ortholattice of closed subspaces of separable real Hilbert space.
We propose a new approach towards proving that the fixed point property for ordered sets is preserved by products. This approach uses a characterization of fixed points in products via isotone relations. First explorations of classes of isotone relations are presented. These first explorations give us hope that this approach could lead to advances on the Product Problem.
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