Flat Hilbert cube manifold pairs

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...

Hilbert manifold - definition *

Even if one is interested only in finite-dimensional manifolds, the need for infinitedimensional manifolds sometimes arises. For example, one approach to study closed geodesics on a manifold is to use Morse theory on its (free) loop space; while for some purposes it is enough to work with finite-dimensional approximations, it is helpful for some finer aspects of the theory to use models of the ...

The design of Hilbert transform pairs of wavelet bases via the flat delay filter

This paper describes a simple procedure, based on spectral factorization, for the design of a pair of orthonormal wavelet bases where the two wavelets form a Hilbert transform pair. The two scaling filters respectively have the numerator and denominator of the flat delay all-pass filter as factors. The design procedure allows for an arbitrary number of zero wavelet moments to be specified. A Ma...

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