This announcement exhibits smooth 4-dimensional manifold triads (W;Mo,Mi) which are s-cobordisms, i.e. the inclusions Mi Ç W, i = 0,1, are simple homotopy equivalences, but are not diffeomorphic or even homeomorphic to a product Mi x [0,1]. The Barden-Mazur-Stallings s-cobordism theorem constitutes one of the foundational stones of modern topology. It asserts, in the smooth, piecewiselinear, or...

There are complex spatio-temporal relationships among cadastral entities. Cadastral spatio-temporal data model should not only describe the data structure of cadastral objects, but also express cadastral spatio-temporal relationships between cadastral objects. In the past, many experts and scholars have proposed a variety of cadastral spatio-temporal data models, but few of them concentrated on...

Abstract The fractal or Hausdorff dimension is a measure of roughness (or smoothness) for time series and spatial data. The graph of a smooth, differentiable surface indexed in Rd has topological and fractal dimension d. If the surface is non-differentiable and rough, the fractal dimension takes values between the topological dimension, d, and d + 1. We review and assess estimators of fractal d...

We prove addition and subspace theorems for asymptotic large inductive dimension. We investigate a transfinite extension of this dimension and show that it is trivial. 0. Asymptotic dimension asdim of a metric space was defined by Gromov for studying asymptotic invariants of discrete groups [1]. This dimension can be considered as asymptotic analogue of the Lebesgue covering dimension dim. Dran...

Topological excitations produce obstructions to making the gauge field smooth everywhere. Therefore, they should appear as singularities in an otherwise smooth gauge. This offers the possibility of identifying such excitations via gaugefixing. After gauge-fixing, the gauge field becomes singular, and the gauge ill-defined, on a sub-manifold characterizing the topological excitations. Even thoug...

Topological dynamics is, roughly, the study of phenomena related to iterations of continuous maps from a metric space to itself. We show how the rewrite relation in term rewriting gives rise to dynamical systems in two distinct, natural ways: (A) One in which any deterministic rewriting strategy induces a dynamical system on the set of finite and infinite terms endowed with the usual metric, an...

It has been known for 30 years that posets with bounded height and with cover graphs of bounded maximum degree have bounded dimension. Recently, Streib and Trotter proved that dimension is bounded for posets with bounded height and planar cover graphs, and Joret et al. proved that dimension is bounded for posets with bounded height and with cover graphs of bounded tree-width. In this paper, it ...