Original Articles

BOUNDED SUBSETS AND WEAK REALCOMPACTNESS CONDITIONS

Published in: Quaestiones Mathematicae
Volume 24 , issue 2 , 2001 , pages: 225–235

DOI: 10.1080/16073606.2001.9639211

Author(s): S. Kundu Department Of Mathematics, Indian Institute of Technology, Delhi, New Delhi, India, , A. B. Raha Stat-Math Division, Indian Statistical Institute, Calcutta, India, , M. A. Swardson Department of Mathematics, Ohio University, Athens, Ohio, USA,

Keywords: Bounded set , zero set , (weak) bz-space , (weak) μ-space , space of pseudo-countable type , unbounded point , untracable point

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Abstract

A subset A of X is bounded if every continuous real-valued function on X is bounded on A. A completely regular Hausdorff space X is said to have the bz-property if every bounded subset of X is contained in a bounded zero subset of X. In this paper, we study the bz-property and its relation to other well known topological properties. We also introduce some new topological properties, all weaker than realcompactness, that are related to the bz-property. The origin of the bz-property lies in a measure-theoretic problem.

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