The Converse Ostrowski Theorem: aspects of compactness
نویسندگان
چکیده
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 Ostrowskitype relate to additive (pseudo)compactness. We give a di¤erent characterization of such sets, in terms of the property of generic subuniversality, arising from the Kestelman-BorweinDitor theorem and relate these to various new forms of compactness. Classi cation: 26A03
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تاریخ انتشار 2007