Manifold - Wikipedia
网页In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an -dimensional manifold, or -manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of -dimensional Euclidean space.
Manifold Definition & Meaning - Merriam-Webster
网页The meaning of MANIFOLD is marked by diversity or variety. How to use manifold in a sentence.
MANIFOLD | English meaning - Cambridge Dictionary
网页MANIFOLD definition: 1. many and of several different types: 2. a pipe or closed space in a machine that has several…. Learn more.
Manifold -- from Wolfram MathWorld
网页2024年8月22日 · A manifold is a topological space that is locally Euclidean (i.e., around every point, there is a neighborhood that is topologically the same as the open unit ball in R^n). To illustrate this idea, consider the ancient belief that the Earth was flat as contrasted with the modern evidence that it is round.
MANIFOLD Definition & Meaning - Dictionary.com
网页noun. something having many varied parts, forms, or features. a copy of a page, book, etc. a chamber or pipe with a number of inlets or outlets used to collect or distribute a fluid.
Manifold | Differential Geometry, Topology & Algebra | Britannica
网页2024年8月16日 · Manifold, in mathematics, a generalization and abstraction of the notion of a curved surface; a manifold is a topological space that is modeled closely on Euclidean space locally but may vary widely in global properties.
网页Definition 1.3. A smooth n-dimensional manifold is a Hausdorff, second count-able, topological space X together with an atlas, A. 1.1 examples Rn or any open subset of Rn is a smooth manifold with an atlas consisting of one chart. The unit sphere Sn = {(x0,x1,...,xn)| Xn i=0 (xi)2 = 1}