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A topographic map of Stowe, Vermont with contour lines This false-color satellite image illustrates topography of the urban core of the New York metropolitan area, with Manhattan at its center. Topography is the study of the forms and features of land surfaces .
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 ...
In mathematics, particularly topology, an atlas is a concept used to describe a manifold. An atlas consists of individual charts that, roughly speaking, describe individual regions of the manifold. In general, the notion of atlas underlies the formal definition of a manifold and related structures such as vector bundles and other fiber bundles.
The terms 'nearby', 'arbitrarily small', and 'far apart' can all be made precise by using the concept of open sets. If we change the definition of 'open set', we change what continuous functions, compact sets, and connected sets are. Each choice of definition for 'open set' is called a topology. A set with a topology is called a topological space.
An equivalent, possibly more intuitive definition when and are metric spaces is as follows: we say an infinite sequence of points {} in a topological space escapes to infinity if, for every compact set only finitely many points are in .
Topographic maps are also commonly called contour maps or topo maps. In the United States, where the primary national series is organized by a strict 7.5-minute grid, they are often called or quads or quadrangles. Topographic maps conventionally show topography, or land contours, by means of contour lines.
This glossary of geography terms is a list of definitions of terms and concepts used in geography and related fields, including Earth science, oceanography, cartography, and human geography, as well as those describing spatial dimension, topographical features, natural resources, and the collection, analysis, and visualization of geographic ...
A coordinate map, a coordinate chart, or simply a chart, of a manifold is an invertible map between a subset of the manifold and a simple space such that both the map and its inverse preserve the desired structure. [2]