Most CAD or other spatial data models, in particular boundary representation models, are called "topological" and represent spatial data by a structured collection of "topological primitives" like edges, vertices, faces, and volumes. These then represent spatial objects in geo-information- (GIS) or CAD systems or in building information models (BIM). Volume objects may then either be represented by their 2D boundary or by a dedicated 3D-element, the "solid". The latter may share common boundary elements with other solids, just as 2D-polygon topologies in GIS share common boundary edges. Despite the frequent reference to "topology" in publications on spatial modelling the formal link between mathematical topology and these "topological" models is hardly described in the literature. Such link, for example, cannot be established by the often cited nine-intersections model which is too elementary for that purpose. Mathematically, the link between spatial data and the modelled "real world" entities is established by a chain of "continuous functions" - a very important topological notion, yet often overlooked by spatial data modellers. This article investigates how spatial data can actually be considered topological spaces, how continuous functions between them are defined, and how CAD systems can make use of them. Having found examples of applications of continuity in CAD data models it turns out that of continuity has much practical relevance for CAD systems.
Database schemes (which, intuitively, are collections of table skeletons) can be viewed as hypergraphs. (A hypergraph is a generalization of an ordinary undirected graph, such that an edge need not contain exactly two nodes, but can instead contain an arbitrary nonzero number of nodes.) Unlike the situation for ordinary undirected graphs, there are several natural, nonequivalent notions of acyclicity for hypergraphs (and hence for database schemes). A large number of desirable properties of database schemes fall into a small number of equivalence classes, each completely characterized by the degree of acyclicity of the scheme. This paper is intended to be an informal introduction, in which the focus is mainly on the originally studied (and least restrictive) degree of acyclicity.