#Topology in Geography
Topology is a broad branch of mathematics used to describe the fundamental structure of a shape or object within a space. Objects can be manipulated by stretching or compressing the shape’s components, but the tearing of or addition to its structure will break topology. According to the rules of topology, a doughnut and a coffee mug are equal.
###Topology example: ![Alt text] (http://i.imgur.com/sBP9p.gif)
Geography utilizes topology to project geometric objects from a 3D sphere onto a 2D coordinate system while allowing the shape to stay intact with some distortion.
###3D Sphere projections to 2D plane: ![Alt text] (http://i.imgur.com/FJmHs.gif)
These representative, geometric objects are also known as vectors which can be simply described as points, lines, and polygons. When building a geographic database, topology becomes a defined set of rules which its objects must follow when creating or validating vectors. Example topology rules in a geodatabase include: polygons must be adjacent with no overlapping or gaps, points must be on line ends, or all line directions in a network must be congruent. The creating, management, and editing of geometry may lead to redundancies, inaccurate analysis, and poor database performance without enforcing topology.
Enterprise GIS (Geographic Information Systems) employs topology to model geometric data and provide QA/QC to its contributors and management. Well architected systems allow spatial relationships to infer object creation; for example, a set of points becomes a polygon’s vertices.
###Points to polygon: ![Alt text] (http://i.imgur.com/jIq0b.png)
Topology in Geography plays two major roles: interpreting 3D features onto 2D planes and preserving the integrity of a geodatabase. Before studying geography and entering the profession, I had never encountered the concept of topology, but I can now appreciate its rules and application to the discipline. Topology allows for improved performance, accuracy, and control in GIS.