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The converse Ostrowski theorem

Bingham, N. H. and Ostaszewski, Adam (2007) The converse Ostrowski theorem. LSE-CDAM-2007-25. London school of economics & political science, London, UK.

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Identification Number: LSE-CDAM-2007-25

Abstract

The Ostrowski theorem in question is that an additive function bounded (above, say) on a set T of positive measure is continuous. In the converse direction, recall that a topological space T is pseudocompact if every function continuous on T is bounded. Thus theorems of `converse Ostrowski' type relate to `additive (pseudo)compactness'. We give a different characterization of such sets, in terms of the property of `generic subuniversality', arising from the Kestelman-Borwein-Ditor theorem.

Item Type: Monograph (Report)
Official URL: http://www.cdam.lse.ac.uk/Reports/
Additional Information: © 2007 London school of economics & political science
Subjects: H Social Sciences > H Social Sciences (General)
Sets: Departments > Mathematics
Date Deposited: 10 Jul 2008 08:38
Last Modified: 11 May 2011 09:34
URI: http://eprints.lse.ac.uk/id/eprint/6832

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