Lecture

Spatial Relations and Topology

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Description

This lecture covers elements related to spatial relations and topology, including the role of topological rules in databases used by geographic information systems. The main focus is on the four primary forms of topological relations: adjacency, connectivity, inclusion, and intersection.

In MOOC

Geographical Information Systems 1

In this first part of the course, we will focus on the digitization and the storage of geodata. In particular, you will learn:

To characterize spatial objects and/or phenomena (territory modeling) with respect to their position in space (through coordinate systems, projections, and spatial relationships) and according to their intrinsic nature (object/vector mode vs. Image/raster mode);
About the different means used to acquire spatial data; including direct measurement, georeferencing images, digitiza

Official source

Related concepts (19)

General topology

In mathematics, general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. The fundamental concepts in point-set topology are continuity, compactness, and connectedness: Continuous functions, intuitively, take nearby points to nearby points.

Final topology

In general topology and related areas of mathematics, the final topology (or coinduced, strong, colimit, or inductive topology) on a set with respect to a family of functions from topological spaces into is the finest topology on that makes all those functions continuous. The quotient topology on a quotient space is a final topology, with respect to a single surjective function, namely the quotient map. The disjoint union topology is the final topology with respect to the inclusion maps.

Order topology

In mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets. If X is a totally ordered set, the order topology on X is generated by the subbase of "open rays" for all a, b in X. Provided X has at least two elements, this is equivalent to saying that the open intervals together with the above rays form a base for the order topology.

Topology

In mathematics, topology (from the Greek words τόπος, and λόγος) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity.

Initial topology

In general topology and related areas of mathematics, the initial topology (or induced topology or weak topology or limit topology or projective topology) on a set with respect to a family of functions on is the coarsest topology on that makes those functions continuous. The subspace topology and product topology constructions are both special cases of initial topologies. Indeed, the initial topology construction can be viewed as a generalization of these.

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