Spaces of valuations as quasimetric domains

Philipp Sünderhauf
<span title="">1998</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uy5mv2ncw5eahkdx47hkrglxmm" style="color: black;">Electronical Notes in Theoretical Computer Science</a> </i> &nbsp;
We de ne a natural quasimetric on the set of continuous valuations of a topological space and investigate it in the spirit of quasimetric domain theory. It turns out that the space of valuations of an (ordinary) algebraic domain D is an algebraic quasimetric domain. Moreover, it is precisely the lower powerdomain of D, where D is regarded as a quasimetric domain. The essential tool for proving these results is a generalization of the Splitting Lemma which c haracterizes the quasimetric for
more &raquo; ... e valuations and holds for valuations on arbitrary topological spaces.
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