The tag has no wiki summary.

learn more… | top users | synonyms

11
votes
0answers
225 views

Are there additive subgroups of reals of dimension 1 with no subgroups of dimension strictly between 0 and 1?

I will use $dimA$ to denote the Hausdorff dimension of a set $A \subseteq \mathbb{R}$. Being a null set means having Lebesgue measure zero. In the 1966 paper "Additive gruppen mit vorgegebener ...
8
votes
0answers
241 views

Ultrapowers of Banach spaces without the continuum hypothesis

Let $\mathcal{U}$ be a non-trivial ultrafilter on the set of integers $\mathbb{N}$, and let $C(K)$ denote the Banach space of continuous functions on a compact $K$. Under the continuum hypothesis CH, ...
5
votes
0answers
350 views

Last Status of Feferman's Conjecture on Indefinite Value of Continuum

The "true" value of $2^{\aleph_0}$ is one of the most fundamental open questions of mathematics and its philosophy. Hundreds of set theoretic results during the last century don't say anything more ...