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There are at least three definitions of "groupoid" currently in use. The first type of groupoid is an algebraic structure on a set with a binary operator. The only ...

If F is a family of more than n bounded closed convex sets in Euclidean n-space R^n, and if every H_n (where H_n is the Helly number) members of F have at least one point in ...

If R is a Noetherian ring, then S=R[X] is also a Noetherian ring.

Any complex measure lambda decomposes into an absolutely continuous measure lambda_a and a singular measure lambda_c, with respect to some positive measure mu. This is the ...

The set lambda of linear Möbius transformations w which satisfy w(t)=(at+b)/(ct+d), where a and d are odd and b and c are even. lambda is a subgroup of the modular group ...

Multivariable calculus is the branch of calculus that studies functions of more than one variable. Partial derivatives and multiple integrals are the generalizations of ...

The Pontryagin number is defined in terms of the Pontryagin class of a manifold as follows. For any collection of Pontryagin classes such that their cup product has the same ...

When can homology classes be realized as the image of fundamental classes of manifolds? The answer is known, and singular bordism groups provide insight into this problem.

The Stiefel-Whitney number is defined in terms of the Stiefel-Whitney class of a manifold as follows. For any collection of Stiefel-Whitney classes such that their cup ...

The product of primes p_n#=product_(k=1)^np_k, (1) with p_n the nth prime, is called the primorial function, by analogy with the factorial function. Its logarithm is closely ...