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A topology is given by a collection of subsets of a topological space X. The smallest topology has two open sets, the empty set emptyset and X. The largest topology contains ...
Let a Gram point g_n be called "good" if (-1)^nZ(g_n)>0, and "bad" otherwise (Rosser et al. 1969; Edwards 2001, p. 180). Then the interval between two consecutive good Gram ...
There does not exist an everywhere nonzero tangent vector field on the 2-sphere S^2. This implies that somewhere on the surface of the Earth, there is a point with zero ...
Let f be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then if f(a)=f(b), then there is at least one point c in (a,b) where f^'(c)=0. ...
Two or more lines are said to be concurrent if they intersect in a single point. Two lines concur if their trilinear coordinates satisfy |l_1 m_1 n_1; l_2 m_2 n_2; l_3 m_3 ...
Two lines in two-dimensional Euclidean space are said to be parallel if they do not intersect. In three-dimensional Euclidean space, parallel lines not only fail to ...
A vector perpendicular to a given vector a is a vector a^_|_ (voiced "a-perp") such that a and a^_|_ form a right angle. In the plane, there are two vectors perpendicular to ...
A subset of an algebraic variety which is itself a variety. Every variety is a subvariety of itself; other subvarieties are called proper subvarieties. A sphere of the ...
The conditional intensity lambda(t) associated to a temporal point process N is defined to be the expected infinitesimal rate at which events are expected to occur around ...
A covering map (also called a covering or projection) is a surjective open map f:X->Y that is locally a homeomorphism, meaning that each point in X has a neighborhood that is ...
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