University of Birmingham > Talks@bham > Topology and Dynamics seminar > Value quantales and Lipschitz constants

Value quantales and Lipschitz constants

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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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