Sentence examples for a minimal element from inspiring English sources

A mapping has a fixed point if is minimalizing, that is, is a minimal element of for all, and if exists in for some whenever is a nonempty chain in.

A contains a minimal element.

(1) A contains a minimal element.

Let be a minimal element of.

We show that has a minimal element.

Then Γ has a minimal element.

Analogously, we can prove the existence of a minimal element.

It follows from Zorn's lemma that has a minimal element.

Therefore, (bar{mathcal{S}} _{P}) is nonempty and bounded below and has a minimal element.

if every non-void subset of P has a minimal element.

The infimum of,, and a minimal element of are defined similarly.