Factoring the Hilbert Cube

2 ' Is Homeomorphic to the Hilbert Cube

Canonical Covers and Dimension of Z-sets in the Hilbert Cube

In this paper we characterize the finite dimensionality of a compact Z-set in the Hilbert cube in terms of the existence of a particular canonical cover in its complement.

On additive and multiplicative Hilbert cubes

Given subset E of natural numbers FS(E) is defined as the collection of all sums of elements of finite subsets of E and any translation of FS(E) is said to be Hilbert cube.We can define the multiplicative analog of Hilbert cube as well. E.G. Strauss proved that for every ε > 0 there exists a sequence with density > 1− ε which does not contain an infinite Hilbert cube. In the present note we giv...

Non - degenerate Hilbert cubes in random sets par

A slight modification of the proof of Szemerédi’s cube lemma gives that if a set S ⊂ [1, n] satisfies |S| ≥ n2 , then S must contain a non-degenerate Hilbert cube of dimension blog2 log2 n− 3c. In this paper we prove that in a random set S determined by Pr{s ∈ S} = 1 2 for 1 ≤ s ≤ n, the maximal dimension of nondegenerate Hilbert cubes is a.e. nearly log2 log2 n+log2 log2 log2 n and determine t...

C0-coarse Geometry of Complements of Z-sets in the Hilbert Cube

Motivated by the Chapman Complement Theorem, we construct an isomorphism between the topological category of compact Z-sets in the Hilbert cube Q and the C0-coarse category of their complements. The C0coarse morphisms are, in this particular case, intrinsically related to uniformly continuous proper maps. Using that fact we are able to relate in a natural way some of the topological invariants ...