Recognizing the topology of the space of closed convex subsets of a Banach space

Taras Banakh, Ivan Hetman, Katsuro Sakai

Let $X$ be a Banach space and $Con{v}_H(X)$ be the space of non-empty closed convex subsets of $X$, endowed with the Hausdorff metric $d_H$. We prove that each connected component of…