  In this paper, we show that there are a totally ordered compact K separable
(K is Rosenthal compact set), a Hausdorff topology T' on C(K) and two closed
subspaces Y1, Y2 of (C(K); Tp) such that (C(K);T') is not universally
measurable, (C(K),Tp) = (Y1,Tp) + (Y2,Tp);(Y1,Tp) is isomorphic to (Y2,Tp), (Yj
,Tp) = (Yj,T'), j=1,2; and Bor((C(K)XC(K),T'XT')) is not equal to
Bor(C(K)),T'))XC(K)),T')) this is the main result of this work. We start this
work to construct totally ordered non metrisable compact sets K(E) from a
reference set E which is totally ordered, and from a positive Borel measure on
E satisfying some reasonable assumptions.
