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Atlas (topology)

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.

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Overview

Charts

Formal definition of atlas

Transition maps

More structure

Advanced semantic analysis

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Map overview Semantic statistics

Atlas (topology)

Nodes35
Edges34
Triples2
Avg. degree1.94
Density0.057143
Components1

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Important terminology Word statistics

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Important terminology

atlas manifold displaystyle transition varphi charts chart definition space called map one notion open euclidean alpha describe differentiable maps structure

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
vector bundlesinstance ofthe notion of atlas underlies the formal definition of a manifold and related structures0.80text
other fiber bundlesinstance ofthe notion of atlas underlies the formal definition of a manifold and related structures0.80text

Related concept clusters Concept neighborhoods

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