# Ball versus distance convexity of metric spaces

Foertsch, T (2004). Ball versus distance convexity of metric spaces. Beiträge zur Algebra und Geometrie, 45(2):481-500.

## Abstract

We consider two different notions of convexity of metric spaces, namely (strict/uniform) ball convexity and (strict/uniform) distance convexity. Our main theorem states that (strict/uniform) distance convexity is preserved under a fairly general product construction, whereas we provide an example which shows that the same does not hold for (strict/uniform) ball convexity, not even when considering the Euclidean product.

## Abstract

We consider two different notions of convexity of metric spaces, namely (strict/uniform) ball convexity and (strict/uniform) distance convexity. Our main theorem states that (strict/uniform) distance convexity is preserved under a fairly general product construction, whereas we provide an example which shows that the same does not hold for (strict/uniform) ball convexity, not even when considering the Euclidean product.