Continua with almost unique hyperspace

HEREDITARILY INDECOMPOSABLE HAUSDORFF CONTINUA HAVE UNIQUE HYPERSPACES 2XAND Cn(X)

Let X be a Hausdorff continuum (a compact connected Hausdorff space). Let 2X (respectively, Cn(X)) denote the hyperspace of nonempty closed subsets of X (respectively, nonempty closed subsets of X with at most n components), with the Vietoris topology. We prove that if X is hereditarily indecomposable, Y is a Hausdorff continuum and 2X (respectively Cn(X)) is homeomorphic to 2Y (respectively, C...

Topology Proceedings 1 (1976) pp. 209-219: SOME PROPERTIES OF WHITNEY CONTINUA IN THE HYPERSPACE C(X)

Continua with spin structure

A continuum Lagrangian-Hamiltonian description of alloys with spin glass structure in magnetic saturation conditions is presented here, paying attention to the interaction between gross deformation and spin substructures. A version of Noether theorem accounting for gyroscopic inertia of spins is proven so that the covariance of the balance of spin interactions and, as a special case, the one of...

Quasicrystals: sections of hyperspace.

It was, and still is, a fundamental law of crystallography that fivefold rotational symmetry and three-dimensional (3D) lattice periodicity are mutually incompatible. With this in mind, the Israeli materials scientist Dan Shechtman did not trust his eyes when he inspected electron diffractograms of rapidly solidified Al-Mn. What he expected to see was either diffraction patterns with sharp Brag...

Achieving User Adaptivity in Hyperspace with HyperContext

HyperContext is a framework for adaptive and adaptable hypertext. In any hyperspace, each piece of information (e.g., contained in a document or node) is normally juxtaposed by other information via links. Two or more hypertext users may encounter the same document although they may have followed different paths to reach it. Those two users may well describe different aspects of the document as...