# Geometry of Banach Spaces, Convexity, Abstract Approximation

Coverings of Banach spaces or their subsets by bounded convex bodies. Extendibility of convex continuous functions from subspaces. Support properties of convex sets in Banach spaces. Properties of metric projections. Existence of generalized centers of finite sets.

**Keywords**

Convex functions; Subdifferential; D.c. functions and mappings; Convex coverings; Polyhedral Banach spaces; Metric projections; Chebyshev centers.

**Pubblications**

C.A. De Bernardi, *Higher Connectedness Properties of Support Points and Functionals of Convex Sets*, Canad. J. Math., to appear (http://dx.doi.org/10.4153/CJM-2012-048-8).

A. Marchese, C. Zanco, *On a question by Corson about point-finite coverings*, Israel J. Math. **189** (2012), 55-63.

C.A. De Bernardi, L. Vesely, *On support points and support functionals of convex sets*, Israel J. Math. **171** (2009), 15-27.

V.P. Fonf, C. Zanco, *Covering a sphere of a Banach space by balls*, Math. Ann. **344** (2009), 939-945.

L. Vesely, L. Zajíček, *On compositions of d.c. functions and mappings*, J. Convex Anal. **16** (2009), 423-439.

**Components**

Members from the Department of Mathematics | ||
---|---|---|

Clemente ZANCO | info | |

Libor VESELY | info | |

Carlo Alberto DE BERNARDI | post doc | info |

Simone FERRARI | PhD | |

Stefania D'ALESSANDRO | PhD | |

Collaborators | ||

Vladimir P. FONF | Ben-Gurion University, Beer-Sheva | |

Luděk ZAJÍČEK | Charles University, Praga, Repubblica Ceca |