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

## Continuity of betweenness functionsAdd to your list(s) Download to your calendar using vCal - Prof. Paul Bankston (Marquette University)
- Thursday 22 March 2018, 14:00-15:00
- Lecture Room B, Department of Mathematics.
If you have a question about this talk, please contact Robert Leek. 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. ## This talk is included in these lists:- Lecture Room B, Department of Mathematics
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