Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2007-25

November 2007 (Revised January 2009)

The Converse Ostrowski Theorem: aspects of compactness

N. H. Bingham and A. J. Ostaszewski

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 and relate these to various new forms of compactness.

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