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An outer measure mu on R^n is Borel regular if, for each set X subset R^n, there exists a Borel set B superset X such that mu(B)=mu(X). The d-dimensional Hausdorff outer ...

A regular local ring is a local ring R with maximal ideal m so that m can be generated with exactly d elements where d is the Krull dimension of the ring R. Equivalently, R ...

Given a function f specified by parametric variables u_1, ..., u_n, a reparameterization f^^ of f over domain U is a change of variables u_i in U->v_i->V via a function phi ...

In a local ring R, there is only one maximal ideal m. Hence, R has only one quotient ring R/m which is a field. This field is called the residue field.

A morphism f:X->Y is said to be separable if K(X) is a separable extension of K(Y).

Starr roses are attractive geometric figures such as those illustrated above.

A subspace A of X is called a strong deformation retract of X if there is a homotopy F:X×I->X (called a retract) such that for all x in X, a in A, and t in I, 1. F(x,0)=x, 2. ...

Let h>=2 and let A_1, A_2, ..., A_h be sets of integers. The sumset A_1+A_2+...+A_h is the set of all integers of the form a_1+a_2+...+a_h, where a_i is a member of A_i for ...

An infinite set, such as the real numbers, which is not countably infinite.

Jacobi theta functions can be used to uniformize all elliptic curves. Jacobi elliptic functions may also be used to uniformize some hyperelliptic curves, although only two ...