2 We are here dealing with the problem of space layout planning. We present an architectural conceptual CAD approach. Starting with design specifications in terms of constraints over spaces, a specific enumeration heuristics leads to a complete set of consistent conceptual design solutions named topological solutions. These topological solutions which do not presume any precise definitive dimen...

We study what we call topological cylindric algebras and tense cylindric algebras defined for every ordinal α. The former are cylindric algebras of dimension α expanded with S4 modalities indexed by α. The semantics of representable topological algebras is induced by the interior operation relative to a topology defined on their bases. Tense cylindric algebras are cylindric algebras expanded by...

As a contribution to higher dimensional spatial data modelling this article introduces a novel approach to spatial database design. Instead of extending the canonical Solid-Face-Edge-Vertex schema of topological data, these classes are replaced altogether by a common type SpatialEntity, and the individual “bounded-by” relations between two consecutive classes are replaced by one separate binary...

We give some lower bounds on the description, sample, and computational complexities of the problems of computing dimension, homology, and topological type of a manifold, and detecting singularities for a polyhedron.

We discuss the systolic inequality for n-dimensional tori, explaining different metaphors that help to organize the proof. The metaphors connect systolic geometry with minimal surface theory, topological dimension theory, and scalar curvature. Mathematics Subject Classification (2000). Primary 53C23

We investigate an analogue of the L 2-Betti numbers for amenable linear sub-shifts. The role of the von Neumann dimension shall be played by the topological entropy.

We prove an extension of the well-known combinatorial-topological lemma of E. Sperner [20] to the case of infinite-dimensional cubes. It is obtained as a corollary to an infinitary extension of the Lebesgue Covering Dimension Theorem .

The concepts of entropy and dimension as applied to dynamical systems are reviewed from a physical point of view. The information dimension, which measures the rate at which the information contained in a probability density scales with resolution, fills a logical gap in the classification of attractors in terms of metric entropy, fractal dimension, and topological entropy. Several examples are...

That rich, unkempt world of wild and tame topology, born in the minds of Antoine and Alexander, recalled from obscurity by Fox, Artin, and Moise, and brought to full bloom by Bing, has spawned a conjecture on the nature of the topological manifold having as one of its minor corollaries the famous double suspension theorem for homology spheres. F. Quinn in the Saturday morning topology seminar o...