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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 ...
Absolutely closed See H-closed Accessible See . Accumulation point See limit point. Alexandrov topology The topology of a space X is an Alexandrov topology (or is finitely generated) if arbitrary intersections of open sets in X are open, or equivalently, if arbitrary unions of closed sets are closed, or, again equivalently, if the open sets are the upper sets of a poset.
In modern mapping, a topographic map or topographic sheet is a type of map characterized by large-scale detail and quantitative representation of relief features, usually using contour lines (connecting points of equal elevation), but historically using a variety of methods.
Whereas a loop has a distinguished point on it, called its basepoint, a free loop lacks such a distinguished point. Formally, let be a topological space. Then a free loop in is an equivalence class of continuous functions from the circle to . Two loops are equivalent if they differ by a reparameterization of the circle.
The term topography originated in ancient Greece and continued in ancient Rome, as the detailed description of a place. The word comes from the Greek τόπος (topos, "place") and -γραφία (-graphia, "writing"). [3]
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.
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A shape and its skeleton, computed with a topology-preserving thinning algorithm. In shape analysis, skeleton (or topological skeleton) of a shape is a thin version of that shape that is equidistant to its boundaries.