# Some observations on filters with properties defined by open covers

@article{HernandezGutierrez2014SomeOO,
title={Some observations on filters with properties defined by open covers},
author={Rodrigo Hern'andez-Guti'errez and P. Szeptycki},
journal={arXiv: General Topology},
year={2014}
}
• Published 21 May 2014
• Mathematics
• arXiv: General Topology
We study the relation between the Hurewicz and Menger properties of filters considered topologically as subspaces of P(\omega) with the Cantor set topology.
7 Citations

### A non-discrete space X with Cp(X) Menger at infinity

• Mathematics
Applied General Topology
• 2019
In a paper by Bella, Tokgös and Zdomskyy it is asked whether there exists a Tychonoff space X such that the remainder of Cp(X) in some compactification is Menger but not σ-compact. In this paper we

### PROBLEMS ON COUNTABLE DENSE HOMOGENEITY

• Mathematics
• 2016
We survey recent development in research on countable dense homogeneity with special emphasis on open problems.

## References

SHOWING 1-10 OF 28 REFERENCES

### Combinatorics of filters and ideals

• Mathematics
• 2010
We study the combinatorial aspects of filters and ideals on countable sets, concentrating on Borel ideals and their interaction with non-definable ones. The basic tools for this study are cardinal

### Countable dense homogeneous filters and the Menger covering property

• Mathematics
• 2014
In this note we present a ZFC construction of a non-meager filter which fails to be countable dense homogeneous. This answers a question of Hern\'andez-Guti\'errez and Hru\v{s}\'ak. The method of the

### MATHIAS FORCING AND COMBINATORIAL COVERING PROPERTIES OF FILTERS

• Mathematics
The Journal of Symbolic Logic
• 2015
Topological characterizations of filters F on ω such that the Mathias forcing adds no dominating reals or preserves ground model unbounded families are given.

### The combinatorics of open covers (II)

• Mathematics
• 1995
We continue to investigate various diagonalization properties for sequences of open covers of separable metrizable spaces introduced in Part I. These properties generalize classical ones of

### Hereditary topological diagonalizations and the Menger-Hurewicz Conjectures

• Mathematics
• 2005
We consider the question of which of the major classes defined by topological diagonalizations of open or Borel covers is hereditary. Many of the classes in the open case are not hereditary already

### Scales, fields, and a problem of Hurewicz

• Mathematics
• 2008
Menger's basis property is a generalization of $\sigma$-comp\-actness and admits an elegant combinatorial interpretation. We introduce a general combinatorial method to construct non $\sigma$-compact

### MENGER'S AND HUREWICZ'S PROBLEMS: SOLUTIONS FROM "THE BOOK" AND REFINEMENTS

We provide simplified solutions of Menger's and Hurewicz's prob- lems and conjectures, concerning generalizations of σ-compactness. The reader who is new to this field will find a self-contained