In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighborhood that is homeomorphic to the Euclidean space of dimension n. In this more precise terminology, a manifold is referred to as an n-manifold. One-dimensional manifolds include lines and circles, but not figure eights (because no neighborhood of their crossing point is homeomorphic to Euclidean 1-space). Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, which can...

In general relativity, the hole argument is an apparent paradox that much troubled Albert Einstein while developing his famous field equations. Some philosophers of physics take the argument to raise a problem for manifold substantialism, a doctrine that the manifold of events in spacetime is a "substance" which exists independently of the metric field defined on it or the matter within it. Other philosophers and physicists disagree with this interpretation, and view the argument as a confusion about gauge invariance and gauge fixing instead. == Einstein's hole argument == In a usual field equation...

Several cities have been given the nickname "Center (or Centre) of the Universe". In addition, several fictional works have described a depicted location as being at the center of the universe. Modern models of the Universe suggest it does not have a center, unlike previous systems which placed Earth (geocentrism) or the Sun (heliocentrism) at the center of the Universe. == Nicknames of places == === Asia === Wudaokou, Beijing (a nickname) === Europe === Perpignan (France) : Salvador Dali considered its train station as the center of the Universe Wolverhampton, UK : Sir Terry Wogan re...

In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical system. The Poisson bracket also distinguishes a certain class of coordinate transformations, called canonical transformations, which map canonical coordinate systems into canonical coordinate systems. A "canonical coordinate system" consists of canonical position and momentum variables (below symbolized by q...