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Prof. Kunzi gave a talk about some questions related with the theory of quasi-metrics, i. e. metrics which don’t satisfy the symmetry axiom. Although these constructions could seem to be artificial, we will try to convince the audience that they are natural and useful structures. In the first part, he spoke about m-splitting quasi-metrics associated with a partially ordered metric space (X,m,<), i. e. quasi-metrics whose symmetrization is m and whose specialization preorder is <. Some questions about these quasi-metrics were also discussed. In the second part, we addressed he origins of the concept of a weightable quasi-metric and its equivalence with a partial metric. He also emphasized its importance in Computer Science.