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A manifold can be constructed by giving a collection of coordinate charts, that is, a covering by open sets with homeomorphisms to a Euclidean space, and patching functions [clarification needed]: homeomorphisms from one region of Euclidean space to another region if they correspond to the same part of the manifold in two different coordinate ...
The rough concept is older. In the 19th and early 20th century, the terms domain and region were often used informally (sometimes interchangeably) without explicit definition. [9] However, the term "domain" was occasionally used to identify closely related but slightly different concepts.
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 combined region of the two sets is called their union, denoted by A ∪ B, where A is the orange circle and B the blue. The union in this case contains all living creatures that either are two-legged or can fly (or both). The region included in both A and B, where the two sets overlap, is called the intersection of A and B, denoted by A ∩ B.
In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. It can be classified also as a tessellation. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators).
When at most three regions meet at a point, the result is a planar graph, but when four or more regions meet at a point, the result can be nonplanar (for example, if one thinks of a circle divided into sectors, with the sectors being the regions, then the corresponding map graph is the complete graph as all the sectors have a common boundary ...
In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. It is closely related to the concepts of open set and interior . Intuitively speaking, a neighbourhood of a point is a set of points containing that point where one can move some amount in any direction away from ...