Consistency of distinct selection principles for tau-covers
Consistency of distinct selection principles for tau-covers
Let be a topological space. Write {\sf S}_1(\{\mathcal O_n\}_{n\in\mathbb{N}),\mathrm{T}) for the property that, from every sequence of covers of the relevant type, one can select a single member from each cover so that the selected family belongs to . Write for the corresponding selection property for sequences of open -covers, where is the collection of open -covers. Consistency conjecture for tau-covers. It is consistent that
The paper notes that implies Rothberger's property , so consistency of Borel's conjecture prevents replacing “consistent” by “provable.” The claim is presented only as a guess, and no resolution of the consistency statement is supplied.
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Sources & referencesView supporting material
Primary source
Boaz Tsaban, “Strong gamma-sets and other singular spaces”, arXiv:math/0208057 (2007).
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