From Wiki.GIS.com

Topology (from the Greek τόπος, “place”, and λόγος, “study”)^[1] is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed. A circle is topologically equivalent to an ellipse (into which it can be deformed by stretching) and a sphere is equivalent to an ellipsoid. Similarly, the set of all possible positions of the hour hand of a clock is topologically equivalent to a circle (i.e., a one-dimensional closed curve with no intersections that can be embedded in two-dimensional space), the set of all possible positions of the hour and minute hands taken together is topologically equivalent to the surface of a torus (i.e., a two-dimensional a surface that can be embedded in three-dimensional space), and the set of all possible positions of the hour, minute, and second hands taken together are topologically equivalent to a three-dimensional object.^[2]

[edit] Topology in GIS

In ESRI ArcGIS geodatabases, a topology is the arrangement that defines how point, line, and polygon features share coincident geometry. For example, street centerlines and census blocks share common geometry, and adjacent soil polygons share their common boundaries.

Topology defines and enforces data integrity rules (for example, there should be no gaps between polygons). It supports topological relationship queries and navigation (for example, navigating feature adjacency or connectivity), supports sophisticated editing tools, and allows feature construction from unstructured geometry (for example, constructing polygons from lines).

Addressing topology is more than providing a data storage mechanism. In ArcGIS, topology includes all of the following six aspects:

1. The geodatabase includes a topological data model using an open storage format for simple features (i.e., feature classes of points, lines, and polygons), topology rules, and topologically integrated coordinates among features with shared geometry. The data model includes the ability to define the integrity rules and topological behavior of the feature classes that participate in a topology.

2. ArcGIS includes topology layers in ArcMap that are used to display topological relationships, errors, and exceptions. ArcMap also includes a rich set of tools for query, editing, validation, and error correction of topologies.

3. ArcToolbox includes a comprehensive set of geoprocessing tools for building, analyzing, managing, and validating topologies.

4. ArcGIS includes advanced software logic to analyze and discover the topological elements in the feature classes of points, lines, and polygons. This includes a rich set of tools to validate, discover, identify, edit, and resolve both the topological graph and the feature coordinates. These tools are heavily used throughout ArcGIS for many workflows and tasks.

5. ArcMap includes a rich editing and data automation framework that is used to create, maintain, and validate topological integrity and to perform shared feature editing.

6. ArcGIS software logic is available in the Desktop, Engine, and Server that can navigate topological relationships, work with adjacency and connectivity, and assemble features from these elements. For example, identify the polygons that share a specific common edge; list the edges that connect at a certain node; navigate along connected edges from the current location; add a new line and "burn" it into the topological graph; split lines at intersections; and create resulting edges, faces, and nodes.

[edit] Elements of a geodatabase topology

In a geodatabase, the following properties are defined for each topology:

• The name of the topology to be created.

• The cluster tolerance used in topological processing operations. The cluster tolerance is often a term used to refer to two tolerances: the x,y tolerance and the z-tolerance. The default value for the cluster tolerance is 10 times the coordinate resolution.

• List of feature classes. First you need a list of the feature classes that will participate in a topology. All must be in the same coordinate system and organized into the same feature dataset.

• The relative accuracy rank of the coordinates in each feature class. If some feature classes are more accurate than others, you will want to assign a higher coordinate rank. This will be used in topological validation and integration. Coordinates of a lower accuracy will be moved to the locations of more accurate coordinates when they fall within the cluster tolerance of one another. Features with the highest accuracy should receive a value of 1, less accurate feature classes a value of 2, even less accurate feature classes a value of 3, and so on.

• A list of topology rules for how features share geometry.

[edit] References