The existence of deep connections between partial metrics and valuations is well known in domain theory. However, the treatment of non-algebraic continuous Scott domains has been not quite satisfactory so far. In this paper we return to the continuous normalized valuations #mu# on the systems of open sets and introduce notions of co-continuity ({U_i, the point i delong to (is member of ) the set I} is a filtered system of open sets #mu(Int(n_i implied by IU_t))=inf_i implied by I #mu#(U_t)) and strong non-degencracy (U is contained in V are open sets => #mu#(U) < #mu#(V)) for such valuations. We call the resulting class of valuations CC-valuations. The first central result of this paper is a construction of CC-valuations for Scott topologies on all continuous dcpo's with countable based. This is a surprising result because neither co-continuous, nor strongly non degenerate valuations are usually possible for ordinary Hausdorff topologies. Another central result is a new construction of partial metrics. Given a continuous Scott domain A and a CC-valuation #mu# on the system of Scott open subsets of A, we construct a continuous partial metric on A yielding the Scott topology as u(x,y)=#mu#(A/(C_x intersect C_y))- #mu#(I_x intersect I_y), where C_x={y iimplied by A|y is contained in = x} and I_x={y implied by A|{x,y}is unbounded}. This construction covers important cases based on the real line and allows to obtain an induced metric on Total(A) without the unpleasant restrictions known from earlier work.
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