English

A universal differentiability set in Banach spaces with separable dual

Functional Analysis 2011-03-29 v1

Abstract

We show that any non-zero Banach space with a separable dual contains a totally disconnected, closed and bounded subset S of Hausdorff dimension 1 such that every Lipschitz function on the space is Fr\'echet differentiable somewhere in S.

Keywords

Cite

@article{arxiv.1103.5094,
  title  = {A universal differentiability set in Banach spaces with separable dual},
  author = {Michael Doré and Olga Maleva},
  journal= {arXiv preprint arXiv:1103.5094},
  year   = {2011}
}

Comments

41 pages, 1 figure

R2 v1 2026-06-21T17:44:50.318Z