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A metric space is a set S with a global distance function (the metric g) that, for every two points x,y in S, gives the distance between them as a nonnegative real number ...

The tangent space at a point p in an abstract manifold M can be described without the use of embeddings or coordinate charts. The elements of the tangent space are called ...

A discrete space is simply a topological space equipped with the discrete topology. A discrete space is always a metric space, namely the metric space with the same ...

Minkowski space is a four-dimensional space possessing a Minkowski metric, i.e., a metric tensor having the form dtau^2=-(dx^0)^2+(dx^1)^2+(dx^2)^2+(dx^3)^2. Alternatively ...

A complex vector bundle is a vector bundle pi:E->M whose fiber bundles pi^(-1)(m) are a copy of C^k. pi is a holomorphic vector bundle if it is a holomorphic map between ...

A connection on a vector bundle pi:E->M is a way to "differentiate" bundle sections, in a way that is analogous to the exterior derivative df of a function f. In particular, ...

A topological space, also called an abstract topological space, is a set X together with a collection of open subsets T that satisfies the four conditions: 1. The empty set ...

The partial differential equation del ^2A=-del xE, where del ^2 is the vector Laplacian.

The following vector integrals are related to the curl theorem. If F=cxP(x,y,z), (1) then int_CdsxP=int_S(daxdel )xP. (2) If F=cF, (3) then int_CFds=int_Sdaxdel F. (4) The ...

The measurable space (S^',S^') into which a random variable from a probability space is a measurable function.