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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 ...

In general, a cross is a figure formed by two intersecting line segments. In linear algebra, a cross is defined as a set of n mutually perpendicular pairs of vectors of equal ...

A metatheorem in mathematical logic also known under the name "conditional proof." It states that if the sentential formula B can be derived from the set of sentential ...

Let f be a finite real-valued function defined on an interval [a,b]. Then at every point in [a,b] except on a set of Lebesgue measure zero, either: 1. There is a finite ...

The descending chain condition, commonly abbreviated "D.C.C.," is the dual notion of the ascending chain condition. The descending chain condition for a partially ordered set ...

The direct limit, also called a colimit, of a family of R-modules is the dual notion of an inverse limit and is characterized by the following mapping property. For a ...

Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube [0,1)^s, the star discrepancy is defined as D_N^*(P)=sup_(J in Upsilon^*)D(J,P), (1) where the local ...

Let S be a semigroup and alpha a positive real-valued function on S such that alpha(st)<=alpha(s)alpha(t) (s,t in S). If l^1(S,alpha) is the set of all complex-valued ...

A division algebra, also called a "division ring" or "skew field," is a ring in which every nonzero element has a multiplicative inverse, but multiplication is not ...

Two sextuples of skew lines on the general cubic surface such that each line of one is skew to one line in the other set. In all, there are 30 points, with two lines through ...