English

An intuitive proof of the Dvoretzky-Hanani theorem in R^2

Functional Analysis 2017-11-15 v1

Abstract

The Dvoretzky-Hanani theorem states that the general term of any perfectly divergent series in a finite dimensional space does not tend to zero. An intuitive proof is provided R2 using a construction that allows us to determine a choice of +/- such that a1+/a2+/a3+/a4...+/an...a_1 +/- a_2 +/- a_3 +/- a_4... +/- a_n... converges to a point in the space if ||a_i|| goes to 0. Extensions to the construction are proposed for the general R^n.

Keywords

Cite

@article{arxiv.1711.04635,
  title  = {An intuitive proof of the Dvoretzky-Hanani theorem in R^2},
  author = {Efstratios Markou},
  journal= {arXiv preprint arXiv:1711.04635},
  year   = {2017}
}