The completeness of a normed space is equivalent to the homogeneity of its space of closed bounded convex sets


  • I. Hetman Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine


completeness, normed spaces, topological homogeneity, closed convex sets
Published online: 2013-06-18


We prove that an infinite-dimensional normed space $X$ is complete if and only if the space $\mathrm{BConv}_H(X)$ of all non-empty bounded closed convex subsets of $X$ is topologically homogeneous.

Article metrics
How to Cite
Hetman, I. The Completeness of a Normed Space Is Equivalent to the Homogeneity of Its Space of Closed Bounded Convex Sets. Carpathian Math. Publ. 2013, 5, 44-46.