Category:Kuratowski's Lemma

This category contains pages concerning Kuratowski's Lemma:

Formulation 1

Let $\struct {S, \preceq}, S \ne \O$ be a non-empty ordered set.

Then every chain in $S$ is the subset of some maximal chain.

Formulation 2

Let $S$ be a set of sets which is closed under chain unions.

Then every element of $S$ is a subset of a maximal element of $S$ under the subset relation.