Open relations and collectionwise normality

Volume 65 / 2017

Valentin Gutev 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.

Authors

  • Valentin GutevDepartment of Mathematics
    Faculty of Science
    University of Malta
    Msida MSD 2080, Malta
    e-mail

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