Mazur intersection property for Asplund spaces |
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| Authors: | Miroslav Ba?á k,Petr Há jek |
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| Affiliation: | a Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
b Mathematical Institute, Czech Academy of Science, ?itná 25, 115 67 Praha 1, Czech Republic |
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| Abstract: | The main result of the present note states that it is consistent with the ZFC axioms of set theory (relying on Martin's Maximum MM axiom), that every Asplund space of density character ω1 has a renorming with the Mazur intersection property. Combined with the previous result of Jiménez and Moreno (based upon the work of Kunen under the continuum hypothesis) we obtain that the MIP renormability of Asplund spaces of density ω1 is undecidable in ZFC. |
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| Keywords: | Mazur intersection property Asplund space Martin's Maximum axiom Fundamental biorthogonal system |
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