# Convex sets, metric space of

The family of compact convex sets (cf. Convex set) in a Euclidean space endowed with the Hausdorff metric:

This space is boundedly compact (cf. Blaschke selection theorem). For analogues of metric spaces of convex sets (other metrizations, non-compact sets, classes of sets, other initial spaces) see [1].

#### References

 [1] B. Grünbaum, "Measures of symmetry for convex sets" , Proc. Symp. Pure Math. , 7 (Convexity) , Amer. Math. Soc. (1963) pp. 233–270