zoom link: https://pitt.zoom.us/j/96207413067
(meeting id 962 0741 3067)
Abstract or Additional Information
We examine how "straight" a metric on (the underlying set of) a continuum is, relative to the betweenness relation that says c lies between a and b precisely when c belongs to every subcontinuum containing both a and b. Ideally, the distance from a to b should be the sum of the distances between a and c, and c and b (or the max, in the case of an ultrametric).
The straightening of a metric is defined; two generating metrics for the continuum topology have topologically equivalent straightenings. If the straightened topology is the same as the original, we say the continuum is straightenable. Peano continua are straightenable; sin 1/x continua, fans with infinitely many end points, and indecomposable continua are not.
Straightenability can be extended to non-metrizable continua via the idea of "straightening a uniformity."