On a problem of Rolewicz about Banach spaces that admit support sets |
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Authors: | Piotr Koszmider |
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Affiliation: | aInstytut Matematyki, Politechnika Łódzka, ul. Wólczańska 215, 90-924 Łódź, Poland |
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Abstract: | We construct an example of a nonseparable Banach space which does not admit a support set.2 It is a consistent (and necessarily independent from the axioms of ZFC) example of a space C(K) of continuous functions on a compact Hausdorff K with the supremum norm. The construction depends on a construction of a Boolean algebra with some combinatorial properties. The space is also hereditarily Lindelöf in the weak topology but it doesn't have any nonseparable subspace nor any nonseparable quotient which is a C(K) space for K dispersed. |
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Keywords: | Banach space Biorthogonal system Banach spaces of continuous functions Independence results |
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