Recall that a Partially Ordered Set (poset) $P$ has the fixed point property (FPP) if any order preserving function $f:P\longrightarrow P$ has a fixed point.

Theorm : Suppose $P$ and $Q$ are posets with FPP and at least on of them is finite then $(P\times Q)$ has FPP.

Note : $(a,b)\le(c,d)$ if and only if $a\le c$ and $b\le d$.

Question : Suppose $P$ and $Q$ are two infinite posets with FPP. Does $(P\times Q)$ have FPP ?