Menger's covering property and groupwise density

Schur-Pair Property and the Structure of Varietal Covering Groups

Groupwise density cannot be much bigger than the unbounded number

We prove that g (the groupwise density number) is smaller or equal to b, the successor of the minimal cardinality of an unbounded subset of ωω. This is true even for the version of g for groupwise dense ideals.

A COVERING PROPERTY IN PRINCIPAL BUNDLES

Let $p:Xlo B$ be a locally trivial principal G-bundle and $wt{p}:wt{X}lo B$ be a locally trivial principal $wt{G}$-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that $wt{G}$ is a covering group of $G$ if and only if $wt{X}$ is a covering space of $X$. Then we conclude that a topological space $X$ with non-simply connected universal...

2 0 M ay 2 00 7 SCALES , FIELDS , AND A PROBLEM OF HUREWICZ

Menger's basis property is a generalization of σ-comp-actness and admits an elegant combinatorial interpretation. We introduce a general combinatorial method to construct non σ-compact sets of reals with Menger's property. Special instances of these constructions give known counterexamples to conjectures of Menger and Hurewicz. We obtain the first explicit solution to the Hurewicz 1927 problem,...

ar X iv : m at h / 05 07 04 3 v 2 [ m at h . G N ] 2 9 Se p 20 06 SCALES , FIELDS , AND A PROBLEM OF HUREWICZ

Menger's basis property is a generalization of σ-comp-actness and admits an elegant combinatorial interpretation. We introduce a general combinatorial method to construct non σ-compact sets of reals with Menger's property. Special instances of these constructions give known counterexamples to conjectures of Menger and Hurewicz. We obtain the first explicit solution to the Hurewicz 1927 problem,...