This is an announcement for the paper "Recognizing the topology of the space of closed convex subsets of a Banach space" by Taras Banakh, Ivan Hetman, and Katsuro Sakai.
Abstract: Let $X$ be a Banach space and $Conv_H(X)$ 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 the space $Conv_H(X)$ is homeomorphic to one of the spaces: a singleton, the real line, a closed half-plane, the Hilbert cube multiplied by the half-line, the separable Hilbert space, or a Hilbert space of density not less than continuum.
Archive classification: math.GT math.FA math.GN math.OC
Mathematics Subject Classification: 57N20, 46A55, 46B26, 46B20, 52B05, 03E65
Remarks: 10 pages
Submitted from: tbanakh@yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.6374
or