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TopoJSON is an extension of GeoJSON that encodes topology. Rather than representing geometries discretely, geometries in TopoJSON files are stitched together from shared line segments called arcs. This technique is similar to Matt Bloch’s MapShaper and the Arc/Info Export format, .e00. TopoJSON eliminates redundancy, allowing related geometries to be stored efficiently in the same file. For example, the shared boundary between California and Nevada is represented only once, rather than being duplicated for both states. A single TopoJSON file can contain multiple feature collections without duplication, such as states and counties. Or, a TopoJSON file can efficiently represent both polygons (for fill) and boundaries (for stroke) as two feature collections that share the same arc mesh.
As a result, TopoJSON is substantially more compact than GeoJSON. The above shapefile of U.S. counties is 2.2M as a GeoJSON file, but only 436K as a boundary mesh, a reduction of 80.4% even without simplification. TopoJSON can also be more efficient to render since shared control points need only be projected once. To further reduce file size, TopoJSON uses fixed-precision delta-encoding for integer coordinates rather than floats. This is similar to rounding coordinate values (e.g., LilJSON), but with greater precision. Like GeoJSON, TopoJSON files are easily modified in a text editor and amenable to gzip compression.
Lastly, encoding topology has numerous useful applications for maps and visualization. It facilitates geometry simplification that preserves the connectedness of adjacent features; this applies even across feature collections, such as simultaneous consistent simplification of state and county boundaries. Topology can also be used for Dorling cartograms and other techniques that need shared boundary information.