A guessing principle from a Souslin tree, with applications to topology

@article{Rinot2021AGP,
  title={A guessing principle from a Souslin tree, with applications to topology},
  author={Assaf Rinot and Roy Shalev},
  journal={Topology and its Applications},
  year={2021}
}

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References

SHOWING 1-10 OF 66 REFERENCES

Two More Hereditarily Separable Non-Lindelöf Spaces

Our method using CH is a blend of two earlier constructions (Hajnal-Juhász [2] and Ostaszewski [4]) of hereditarily separable (HS), regular, non-Lindelöf, first countable spaces. [4] produces a much

On countably paracompact spaces

. A topological space X is countably paracompact if and only if X satisfies the condition (A): For any decreasing sequence { F i } of non-empty closed sets with (cid:31) ∞ i =1 F i = ∅ there exists a

Forcing positive partition relations

We show how to force two strong positive partition relations on u, and use them in considering several well-known open problems. In [32] Sierpiñski proved that the well-known Ramsey Theorem [27] does

Proper and Improper Forcing

This work deals with set-theoretic independence results (independence from the usual set-theoretic ZFC axioms), in particular for problems on the continuum. Consequently, the theory of iterated

The Souslin problem

Preliminaries.- Souslin's hypothesis.- The combinatorial property ?.- Homogeneous souslin trees and lines.- Rigid souslin trees and lines.- Martin's axiom and the consistency of SH.- Towards

Countably Compact Spaces and Martin's Axiom

  • W. Weiss
  • Mathematics
    Canadian Journal of Mathematics
  • 1978
The relationship between compact and countably compact topological spaces has been studied by many topologists. In particular an important question is: “What conditions will make a countably compact

A normal space X for which X×I is not normal

In [l ] C. Dowker gave a number of interesting characterizations of normal Hausdorff spaces whose cartesian product with the closed unit interval is not normal. Thus, such a space is often called a
...