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Geospatial topology is the study and application of qualitative spatial relationships between geographic features, or between representations of such features in geographic information, such as in geographic information systems (GIS). [1] For example, the fact that two regions overlap or that one contains the other are examples of topological ...
A geographic information system (GIS) consists of integrated computer hardware and software that store, manage, analyze, edit, output, and visualize geographic data. [1] [2] Much of this often happens within a spatial database; however, this is not essential to meet the definition of a GIS. [1]
Because the world is much more complex than can be represented in a computer, all geospatial data are incomplete approximations of the world. [9] Thus, most geospatial data models encode some form of strategy for collecting a finite sample of an often infinite domain, and a structure to organize the sample in such a way as to enable interpolation of the nature of the unsampled portion.
The Database of Original & Non-Theoretical Uses of Topology (DONUT) is a database of scholarly articles featuring practical applications of topological data analysis to various areas of science. DONUT was started in 2017 by Barbara Giunti, Janis Lazovskis, and Bastian Rieck, [ 126 ] and as of October 2023 currently contains 447 articles. [ 127 ]
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
Because a grid is a sample of a continuous space, raster data is most commonly used to represent geographic fields, in which a property varies continuously or discretely over space. Common examples include remote sensing imagery, terrain/elevation, population density, weather and climate, soil properties, and many others. Raster data can be ...
where is the dimension of the intersection (∩) of the interior (I), boundary (B), and exterior (E) of geometries a and b.. The terms interior and boundary in this article are used in the sense used in algebraic topology and manifold theory, not in the sense used in general topology: for example, the interior of a line segment is the line segment without its endpoints, and its ...
A geographic information system (GIS) can recognize and analyze the spatial relationships that exist within digitally stored spatial data. These topological relationships allow complex spatial modelling and analysis to be performed. Topological relationships between geometric entities traditionally include adjacency (what adjoins what ...