A CONE-THEORETIC BARYCENTER EXISTENCE THEOREM.
| Autor: | GOUBAULT-LARRECQ, JEAN, XIAODONG JIA |
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| Zdroj: | Logical Methods in Computer Science (LMCS); 2024, Vol. 20 Issue 4, p7:1-7:15, 15p |
| Abstrakt: | We show that every continuous valuation on a locally convex, locally convexcompact, sober topological cone C has a barycenter. This barycenter is unique, and the barycenter map ß is continuous, hence is the structure map of a Vw-algebra, i.e., an Eilenberg-Moore algebra of the extended valuation monad on the category of T0 topological spaces; it is, in fact, the unique Vw-algebra that induces the cone structure on C. [ABSTRACT FROM AUTHOR] |
| Databáze: | Complementary Index |
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