arXiv subjects
Publications and source records attributed to Ondřej Kurka.
If a separable Banach space contains an isometric copy of every separable reflexive Fréchet smooth Banach space, then it contains an isometric copy of every separable Banach space. The same conclusion holds if we consider separable Banach spaces with Fréchet smooth dual space. This improves a result of G. Godefroy and N. J. Kalton.
In spite of the Lebesgue density theorem, there is a positive $δ$ such that, for every non-trivial measurable set $S$ of real numbers, there is a point at which both the lower densities of $S$ and of the complement of $S$ are at least $δ$. The problem of determining the supremum of possible values of this $δ$ was studied in a paper of V. I. Kolyada, as well as in some recent papers. We solve this problem in the present work.