Estimados compañeros, el próximo lunes 26 de junio a las 12:00 en el seminario del IUMPA, Hans-Peter A. Künzi,de la Universidad de Ciudad del Cabo (Sudáfrica), impartirá la charla titulada “Studies about extensions of T0-quasi-metrics”
Estáis todos invitados.
Let (X, m, ≤) be a partially ordered metric space, that is, a metric space (X, m) equipped with a partial order ≤ on X.
We say that a T0-quasi-metric d on X is m-splitting provided that d∨d −1 = m. Furthermore d is said to be (X, m, ≤) producing provided that d is msplitting
and the specialization order of d is equal to ≤.
It is easy to see that if (X, m, ≤) is a partially ordered metric space that is produced by a T0-quasi-metric and ≤ is a total order, then there exists exactly
one producing T0-quasi-metric on X. We first shall give an example that shows that a partially ordered metric space can be uniquely produced by a T0-quasimetric although ≤ is not total.
Then we discuss solutions to the following two problems: Let (X, m, ≤) be a partially ordered metric space and A a subset of X.
(1) Suppose that d is a T0-quasi-metric on A which is m|(A × A)-splitting.
When can d be extended to an m-splitting T0-quasi-metric de on X?
(2) Suppose that d is a T0-quasi-metric on A which is (A, m|(A × A), ≤
|(A×A)) producing. When can d be extended to a T0-quasi-metric deon X that
produces (X, m, ≤)?