Topological Relationships between spatial objects is a very important topic for spatial data organization, reasoning, query, analysis and updating in Geographic Information Systems (GIS). The most popular models in current use have fundamental deficiency. In this paper, a whole-based approach is pursued to model binary topological relationships between spatial objects, in which (i) a spatial ob...

A concept of entropy production associated with continuous topolog-ical evolution is deduced (without statistics) from the fact that Cartan-Hilbert 1-form of Action defines a non-equilibrium symplectic system of Pfaff Topological dimension 2n+2. The differential entropy, dS, is composed of the interior product of the non-canonical components of momentum with the components of the differential v...

In this paper we study topological invariants of a class of random groups. Namely, we study right angled Artin groups associated to random graphs and investigate their Betti numbers, cohomological dimension and topological complexity. The latter is a numerical homotopy invariant reflecting complexity of motion planning algorithms in robotics. We show that the topological complexity of a random ...

We are here dealing with the problem of space layout planning. We present an approach based on an intermediate topological level with dynamic space ordering (dso) heuristics. Our software ARCHiPLAN proceeds through a number of steps. First, all the topologically different solutions, without presuming any precise dimension, are enumerated. Next, we may evolve in this topological solution space, ...

We present an ontology consisting of a theory of spatial dimension and a theory of dimension-independent mereological and topological relations in space. Though both are fairly weak axiomatizations, their interplay suffices to define various mereotopological relations and to make any necessary dimension constraints explicit. We show that models of the INCH Calculus and the Region-Connection Cal...

We prove that each analytic set in R contains a universally null set of the same Hausdorff dimension and that each metric space contains a universally null set of Hausdorff dimension no less than the topological dimension of the space. Similar results also hold for universally meager sets. An essential part of the construction involves an analysis of Lipschitzlike mappings of separable metric s...

We study the inverse resonance problem for conformally compact manifolds which are hyperbolic outside a compact set. Our results include compactness of isoresonant metrics in dimension two and of isophasal negatively curved metrics in dimension three. In dimensions four or higher we prove topological finiteness theorems under the negative curvature assumption.

The canonical structure of higher dimensional pure Chern-Simons theories is analysed. It is shown that these theories have generically a non-vanishing number of local degrees of freedom, even though they are obtained by means of a topological construction. This number of local degrees of freedom is computed as a function of the spacetime dimension and the dimension of the gauge group.

We give a simple upper bound for the upper box dimension of a forward invariant set of a C1-diffeomorphism of R. This result can be extended to the class of C1-mappings with finite topological degree. We apply these results to provide estimates for the dimension of the Hénon attractor and Julia sets in two complex variables. AMS classification scheme number: 37C45

Using certain ideas connected with the entropy theory, several kinds of dimensions are introduced for arbitrary topological spaces. Their properties are examined, in particular, for normal spaces and quasi-discrete ones. One of the considered dimensions coincides, on these spaces, with the Čech-Lebesgue dimension and the height dimension of posets, respectively.