Research Article

The order bidual of C(X) for a realcompact space

Published in: Quaestiones Mathematicae
Volume 47 , issue sup1 , 2024 , pages: 101–119

DOI: 10.2989/16073606.2023.2287816

Author(s): Marcel de Jeu Mathematical Institute, Leiden University, the Netherlands , Jan Harm van der Walt University of Pretoria, South Africa

Keywords: Primary: 46E05 , Secondary: 46A40 , 46M40 , Vector lattices , continuous functions , biduals , direct limits , inverse limits

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Abstract

It is well known that the bidual of C(X) for a compact space X, supplied with the Arens product, is isometrically isomorphic as a Banach algebra to for some compact space . The space is unique up to homeomorphism. We establish a similar result for realcompact spaces: The order bidual of C(X) for a realcompact space X, when supplied with the Arens product, is isomorphic as an f-algebra to for some realcompact space . The space is unique up to homeomorphism.

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