## Open relations and collectionwise normality

### Volume 65 / 2017

Bulletin Polish Acad. Sci. Math. 65 (2017), 69-79
MSC: 54C60, 54D15, 54B20, 54C20.
DOI: 10.4064/ba8097-4-2017
Published online: 8 June 2017

#### Abstract

Using the framework of discrete-valued relations, we give a simple proof of a theorem obtained by Stoyan Nedev. This theorem provides a generalisation of an element in the proof of Dowker’s extension theorem, which is essential for constructing continuous selections of set-valued mappings defined on collectionwise normal spaces. Using this relationship, we also give a simple proof of the Dowker’s theorem.