University of Birmingham > Talks@bham > Topology and Dynamics Seminar >  Continuity of betweenness functions

Continuity of betweenness functions

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A ternary relational structure (X,[.,.]), interpreting a notion of betweenness, gives rise to the family of intervals, with interval [a,b] being defined as the set of elements of X between a and b. Under very reasonable circumstances, X is also equipped with some topological structure, in such a way that each interval is a closed nonempty subset of X. The question then arises as to the continuity behavior—within the hyperspace context—of the betweenness function {x,y}—>[x,y]. In this talk we concentrate on metric spaces and the Menger interpretation of betweenness: z lies between x and y if d(x,y) = d(x,z)+d(z,y).

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

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