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A collection of open sets of a topological space whose union contains a given subset. For example, an open cover of the real line, with respect to the Euclidean topology, is ...

An open interval is an interval that does not include its end points. The open interval {x:a<x<b} is denoted (a,b), although the nonstandard notation ]a,b[ is sometimes also ...

A noncompact manifold without boundary.

A pair of quantities (a, b) where ordering is significant, so (a, b) is considered distinct from (b, a) for a!=b.

The central point (r=0) in polar coordinates, or the point with all zero coordinates (0, ..., 0) in Cartesian coordinates. In three dimensions, the x-axis, y-axis, and z-axis ...

In a space E equipped with a symmetric, differential k-form, or Hermitian form, the orthogonal sum is the direct sum of two subspaces V and W, which are mutually orthogonal. ...

Given a pair of orthologic triangles, the point where the perpendiculars from the vertices of the first to the sides of the second concur and the point where the ...

The plane spanned by the three points x(t), x(t+h_1), and x(t+h_2) on a curve as h_1,h_2->0. Let z be a point on the osculating plane, then [(z-x),x^',x^('')]=0, where ...

An outcome is a subset of a probability space. Experimental outcomes are not uniquely determined from the description of an experiment, and must be agreed upon to avoid ...

An "overdot" is a raised dot appearing above a symbol most commonly used in mathematics to indicate a derivative taken with respect to time (e.g., x^.=dx/dt). The expression ...