Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0581.41028
Zajíček, L.
On the Fréchet differentiability of distance functions. (English)
[J] Rend. Circ. Mat. Palermo, II. Ser., Suppl. 5, 161-165 (1984).

Let X be a real Banach space with a uniformly Fréchet differentiable norm and let $X\sp*$ be separable. Let M be an arbitrary nonempty closed subset of X. Then the distance function $d\sb M$ is Fréchet differentiable at all points of $X\setminus M$ except those which belong to an angle small set. Note that any angle small set is $\sigma$-porous and consequently it is of the first category.

MSC 2000:: *41A65 Abstract approximation theory
46G05 Derivatives, etc. (functional analysis)
46B20 Geometry and structure of normed spaces

Keywords: Fréchet derivative; sigma porous set; Banach space; angle small set

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]