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A SEPARATION RESULT FOR COUNTABLE UNIONS OF BOREL RECTANGLES
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- Journal:
- The Journal of Symbolic Logic / Volume 84 / Issue 2 / June 2019
- Published online by Cambridge University Press:
- 22 February 2019, pp. 517-532
- Print publication:
- June 2019
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We provide dichotomy results characterizing when two disjoint analytic binary relations can be separated by a countable union of
${\bf{\Sigma }}_1^0 \times {\bf{\Sigma }}_\xi ^0$ sets, or by a 
${\bf{\Pi }}_1^0 \times {\bf{\Pi }}_\xi ^0$ set.
Structure of the Set of Norm-attaining Functionals on Strictly Convex Spaces
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- Journal:
- Canadian Mathematical Bulletin / Volume 54 / Issue 2 / 01 June 2011
- Published online by Cambridge University Press:
- 20 November 2018, pp. 302-310
- Print publication:
- 01 June 2011
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- Article
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Let
$X$ be a separable non-reflexive Banach space. We show that there is no Borel class which contains the set of norm-attaining functionals for every strictly convex renorming of $X$.
