The union of two Hilbert cubes meeting in a Hilbert cube need not be a Hilbert cube

Factoring the Hilbert Cube

In 1964, R. D. Anderson announced [ l ] that the product of a countably infinite collection of dendra is a Hilbert cube (a dendron being a nondegenerate, uniquely arcwise connected, Peano continuum). He and R. H. Bing conjectured in [4] that a countably infinite product of compact contractible complexes is a Hilbert cube. The purpose of this note is to announce the following theorems which affi...

Fake Boundary Sets in the Hilbert Cube

For each positive integer n, a o-Z-set B„ in the Hilbert cube 7°° is constructed whose complement s„ = Ix — B„ is not homeomorphic to the pseudointerior j of the Hilbert cube though sn and B„ satisfy: (i) every compact subset of s„ is a Z-set in s„; (ii) s„ X s„ is homeomorphic to s; (iii) Bn admits small maps 7°° -» B„; (iv) s„ satisfies the discrete «-cells property; and (v) Bn is locally (n ...

2 ' Is Homeomorphic to the Hilbert Cube

Knowledge Creation as a Square Dance on the Hilbert Cube

This paper presents a micro-model of knowledge creation through the interactions among a group of people. Our model incorporates two key aspects of the cooperative process of knowledge creation: (i) heterogeneity of people in their state of knowledge is essential for successful cooperation in the joint creation of new ideas, while (ii) the very process of cooperative knowledge creation a¤ects t...

The Motive of the Hilbert Cube X [ 3 ]

The Hilbert scheme X [3] of length-3 subschemes of a smooth projective variety X is known to be smooth and projective. We investigate whether the property of having a multiplicative Chow– Künneth decomposition is stable under taking the Hilbert cube. This is achieved by considering an explicit resolution of the rational map X 3 99K X [3]. The case of the Hilbert square was taken care of in Shen...