Finding subsets front page

Quick description

This page contains links to articles that are about techniques for finding subsets with given properties of sets such as $\mathbb{N}$ , $\mathbb{R}$ , $\mathbb{R}^2$ , the complete graph on $n$ vertices, the discrete cube, or the set of all subsets of $\mathbb{N}$ . It is not about finding structured subsets such as subgroups or subspaces, so the techniques have a combinatorial flavour.

The articles

Just-do-it proofs

How to use Zorn's lemma

Transfinite induction

How to use the continuum hypothesis

Finding small nets Quick description ( A $\delta$ -net of a metric space $X$ is a subset $\Delta\subset X$ such that for every $x\in X$ there exists $y\in\Delta$ such that $d(x,y)\leq\delta$ . It is often useful to have a small $\delta$ -net for a metric space. This article discusses a few techniques for finding them, giving particular reference to an idea that can be summarized by the following slogan: a maximal separated set is a net. )