Hyperspaces Homeomorphic to Hilbert Space

A Rigid Space Homeomorphic to Hilbert Space

A rigid space is a topological vector space whose endomorphisms are all simply scalar multiples of the identity map. This is in sharp contrast to the behavior of operators on `2, and so rigid spaces are, from the viewpoint of functional analysis, fundamentally different from Hilbert space. Nevertheless, we show in this paper that a rigid space can be constructed which is topologically homeomorp...

The Space of Lelek Fans in the Cantor Fan Is Homeomorphic to Hilbert Space

We show that the space of all Lelek fans in a Cantor fan, equipped with the Hausdorff metric, is homeomorphic to the separable Hilbert space. This result is a special case of a general theorem we prove about spaces of upper semicontinuous functions on compact metric spaces that are strongly discontinuous.

2 ' Is Homeomorphic to the Hilbert Cube

Introduction to Hilbert Space Frames

We present an introduction to Hilbert space frames. A frame is a generalization of a basis that is useful, for example, in signal processing. It allows us to expand Hilbert space vectors in terms of a set of other vectors that satisfy a certain “energy equivalence” condition. This condition guarantees that any vector in the Hilbert space can be reconstructed in a numerically stable way from its...

Clustering via Hilbert space

We discuss novel clustering methods that are based on mapping data points to a Hilbert space by means of a Gaussian kernel. The *rst method, support vector clustering (SVC), searches for the smallest sphere enclosing data images in Hilbert space. The second, quantum clustering (QC), searches for the minima of a potential function de*ned in such a Hilbert space. In SVC, the minimal sphere, when ...