Optimal sequences of continuous functions converging to a Baire-1 function |
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| Authors: | S.A. Argyros V. Kanellopoulos |
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| Affiliation: | (1) Department of Mathematics, National Technical University of Athens, 157 80, Athens, Greece (e-mail: sargyros@math.ntua.gr,bkanel@math.ntua.gr) , GR |
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| Abstract: | A proof of Rosenthal's co- index conjecture is given. Our approach uses optimal sequences of continuous functions converging to a Baire-1 function. Their existence is obtained by the ”optimal sequences theorem” stated and proved here. For a sequence of functions and a countable ordinal, the variation is also introduced. If pointwise converges to f the relation between and is completely clarified. Finally, optimal sequences associated to a Baire-1 function are defined and their existence for every Baire-1 function is provided. Received: 10 November 2000 / Revised version: 12 March 2002 / Published online: 5 September 2002 |
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