### Reexamined: Normal quasi-uniformity elegantly defined

Today, I have proved another formula for this (hopefully now correct):

Theorem An endoreloid \$latex f\$ is normal iff \$latex \mathsf{Compl} (\mathsf{FCD}) f^{- 1} \circ \mathsf{CoCompl} (\mathsf{FCD}) f \sqsubseteq \mathsf{CoCompl} (\mathsf{FCD}) f \circ (\mathsf{FCD}) f.\$

The above formula also applies to any quasi-uniformity \$latex f\$.

The proof of the theorem is currently available in this PDF file.

Read my free ebook to understand formulas like this.

## 2 thoughts on “Reexamined: Normal quasi-uniformity elegantly defined”

1. From this formula it also follows that normality is determined by the underlying proximity and does not need particular uniformity.

2. Oh well, wrong. See my manuscript instead.