Value quantales and Lipschitz constants

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• Dr. Ittay Weiss (University of Portsmouth)
• Thursday 16 May 2019, 13:00-14:00
• Lecture Theater C, Watson Building.

If you have a question about this talk, please contact Tony Samuel.

In 1997 Flagg introduced the concept of a value quantale, a certain ordered structure distilling key properties of the structure of [0,\infty]. Allowing a metric space to take values in a value quantale rather than insisting on the distances landing in [0,\infty] bears a remarkable consequence: All topological spaces are metrisable. As a result, Flagg’s formalism offers a unification of topology and metric geometry. I will sketch the proof of the result and present recent results emanating from the unified perspective. In particular, a Lipschitz ‘machine’ will be presented; a functor from diagrams of value quantales that produces a category of spaces and mappings with a suitable notion of Lipschitz constant. The classical notion is recovered by running the machine on a certain simple diagram.

This talk is part of the Topology and Dynamics Seminar series.

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• Lecture Theater C, Watson Building
• School of Mathematics Events
• Topology and Dynamics Seminar

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