Through planar enforcement, spatial features can be represented through nodes (0-dimensional cells) edges, sometimes called arcs (one-dimensional cells) or polygons (two-dimensional cells). Mathematical topology assumes that geographic features occur on a two-dimensional plane. Today, topology in GIS is generally defined as the spatial relationships between adjacent or neighboring features. The problem that led to Euler's work in this area, known as "The Seven Bridges of Königsberg," is described in the accompanying article "Conundrum Inspires Topology." More recently, the United States Census Bureau, while preparing for the 1970 census, pioneered the application of mathematical topology to maps to reduce the errors in tabulating massive amounts of census data. In 1736, the mathematician Leonhard Euler published a paper that arguably started the branch of mathematics known as topology. Why should GIS users care about topology? What are the advantages and disadvantages of storing polygon data in shapefiles rather than coverages? But ask these same folks about how topology is handled in shapefiles and the nodding heads give way to shrugging shoulders. When asked if topology is a key concept of GIS, most GIS users will nod their heads in agreement.
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