Research Article

The Banaschewski compactification of an approach space is of Wallman-Shanin-type

Published in: Quaestiones Mathematicae
Volume 44 , issue 7 , 2021 , pages: 905–921

DOI: 10.2989/16073606.2020.1753846

Author(s): E. Colebunders , Belgium , M. Sioen , Belgium

Keywords: 54D35 , 54C20 , 54F50 , 54D35 , 54C20 , 54F50

Abstract

For a topological zero-dimensional Hausdorff space (X, ) it is well known that the Banaschewski compactification ζ(X, ) is of Wallman-Shanin-type, meaning that there exists a closed basis (the collection of all clopen sets), such that the Wallman-Shanin compactification with respect to this closed basis is isomorphic to ζ(X, ).

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