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Manifold — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Manifold
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T11:46:15.190Z
SHA-256 of the archived text: 71dc50581e53b7b63ed9350135b924e3da8d49f4167d5beacfe67b1f0f06411f
Stable URL of this page: https://metraipolis.com/documento/dc_4e77f303aaec

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Manifold — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Manifold (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_4e77f303aaec (Metraipolis archive dc_4e77f303aaec, sha256 71dc50581e53b7b63ed9350135b924e3da8d49f4167d5beacfe67b1f0f06411f)

BibTeX

@misc{dc4e77f303aaec,
  title = {Manifold — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Manifold},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_4e77f303aaec; sha256 71dc50581e53b7b63ed9350135b924e3da8d49f4167d5beacfe67b1f0f06411f},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Manifold. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional manifold, or n {\displaystyle n} -manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of n {\displaystyle n} -dimensional Euclidean space. One-dimensional manifolds include lines and circles, but not self-crossing curves such as a figure-eight. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, and also the Klein bottle and real projective plane. The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows complicated structures to be described in terms of well-understood topological properties of simpler spaces. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. The concept has applications in computer-graphics given the need to associate pictures with coordinates (e.g. CT scans). Manifolds can be equipped with additional structure. One important class of manifolds are differentiable manifolds; their differentiable structure allows calculus to be done. A Riemannian metric on a manifold allows distances and angles to be measured. Symplectic manifolds serve as the phase spaces in the Hamiltonian formalism of classical mechanics, while four-dimensional Lorentzian manifolds model spacetime in general relativity. The study of manifolds requires working knowledge of calculus and topology.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «topology»).
Fonte: Wikipedia in inglese, voce «Manifold» — https://en.wikipedia.org/wiki/Manifold
Wikidata Q203920 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q203920
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Manifold?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1369450001, consultata il 2026-10-07T11:20:21.598Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 0f28934b3b35575f3d1da31d9c895d8c8f39a423a10e029b5434a6a09c6c0b56