Preserving affine baire classes by perfect affine maps |
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Authors: | Ondřej FK Kalenda |
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Institution: | Charles University in Prague, Faculty of Mathematics and Physics, Department of Mathematical Analysis, Sokolovská 83, 186 75, Praha 8, Czech Republic. E-Mail kalenda@karlin.mff.cuni.cz |
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Abstract: | Let ? : X → Y be an affine continuous surjection between compact convex sets. Suppose that the canonical copy of the space of real-valued affine continuous functions on Y in the space of real-valued affine continuous functions on X is complemented. We show that if F is a topological vector space, then f : Y → F is of affine Baire class α whenever the composition f ? ? is of affine Baire class α. This abstract result is applied to extend known results on affine Baire classes of strongly affine Baire mappings. |
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Keywords: | 46A55 26A21 54H05 |
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