Segments and Convexity in Metric Spaces

This talk is based on my work that is currently under submission to the Rose-Hulman Undergraduate Mathematics Journal. We are usually interested in studying convex sets in vector spaces. However, relevant research has shown that a meaningful notion of convex sets can be introduced to metric spaces, based on a more fundamental notion of a metric segment. In this talk, we will explore the properties of metric segments and convex sets in metric spaces. We will discuss the main theorems of my paper that indicate a link between the notions of a U-, directed, Menger convex, and strictly convex metric space. Finally, we will conclude the talk by exploring how convex sets in a metric space interact with the inherent topology of the metric space.

For more information and to register, visit the Math Table website.