269 Citations
Several comments about the combinatorics of τ-cover
- Mathematics
- 2007
In a previous work with Mildenberger and Shelah, we showed that the combinatorics of the selection hypotheses involving τ-covers is sensitive to the selection operator used. We introduce a natural…
Selection principles and the Minimal Tower problem
- Mathematics
- 2003
We study diagonalizations of covers using various selectionprinciples, where the covers are related to linearquasiorderings ( -covers).This includes: equivalences and nonequivalences,combinatorial…
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…
Algebra, selections, and additive Ramsey theory
- Mathematics
- 2014
Hindman's celebrated Finite Sums Theorem, and its high-dimensional version due to Milliken and Taylor, are extended from covers of countable sets to covers of arbitrary topological spaces with…
References
SHOWING 1-10 OF 88 REFERENCES
Combinatorics of Open Covers (III): Games, C p ( X )
- Mathematics
- 1997
Some of the covering properties of spaces as defined in Parts I and II are here characterized by games. These results, applied to function spaces Cp(X) of countable tightness, give new…
On a question of Archangelskij concerning Lindelöf spaces with countable pseudocharacter
- Mathematics
- 1985
We give a negative solution to Archangelskij's problem by showing that there exists a Lindelof space with countable pseudocharacter which does not admit a continuous one-to-one mapping onto a first…
On normal Agassiz systems of algebras
- Mathematics
- 1978
The concept of Agassiz system of algebras and Agassiz sum was introduced by G. Gratzer and J. Sichler in [3]. In this paper we intend to discuss a modification of the concepts above which seems to be…