When does the Haver property imply selective screenability

@article{Babinkostova2007WhenDT,
  title={When does the Haver property imply selective screenability},
  author={Liljana Babinkostova},
  journal={Topology and its Applications},
  year={2007},
  volume={154},
  pages={1971-1979}
}
  • L. Babinkostova
  • Published 1 May 2007
  • Mathematics, Economics
  • Topology and its Applications
PRODUCTS AND SELECTION PRINCIPLES
We study when the product of separable metric spaces has the selective screenability property, the Menger property, or the Rothberger property. Our results imply the product of a Lusin set and (1) a
A METRIC SPACE WITH THE HAVER PROPERTY WHOSE SQUARE FAILS THIS PROPERTY
Haver introduced the following property of metric spaces (X, d): for each sequence 1, 2, . . . of positive numbers there exist collections V1,V2, . . . of open subsets of X, the union ⋃ i Vi of which
A metric space with the Haver property whose square fails this property
Haver introduced the following property of metric spaces (X,d): for each sequence ∈ 1 ,∈ 2 ;.. of positive numbers there exist collections ν 1 , ν 2 ,. of open subsets of X, the union ∪ i ν i of
Selective Screenability and the Hurewicz Property
We characterize the Hurewicz covering property in metrizable spaces in terms of properties of the metrics of the space. Then we show that a weak version of selective screenability, when combined with
Selective Strong Screenability
TLDR
It is found that a great deal of the proofs about selective screenability readily carry over to proofs for the analogous version for selective strong screenability.
Selection Principles and Baire spaces
We prove that if X is a separable metric space with the Hurewicz covering property, then the Banach-Mazur game played on X is determined. The implication is not true when "Hurewicz covering property"
Topological groups and covering dimension
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