Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592292 | Journal of Functional Analysis | 2009 | 19 Pages |
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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