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Combinatorics Of Open Covers Vi: Selectors For Sequences Of Dense Sets, Marion Scheepers

Mathematics Faculty Publications and Presentations

We consider the following two selection principles for topological spaces:

[Principle 1:] { For each sequence of dense subsets, there is a sequence of points from the space, the n-th point coming from the n-th dense set, such that this set of points is dense in the space;

[Principle 2:]{ For each sequence of dense subsets, there is a sequence of finite sets, the n-th a subset of the n-th dense set, such that the union of these finite sets is dense in the space.

We show that for separable metric space X one of these principles holds for the …