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A field of extremals is a plane region which is simply connected by a one-parameter family of extremals. The concept was invented by Weierstrass.

A property of a space which is also true of each of its subspaces. Being "first-countable" is hereditary, but having a given genus is not.

alpha is called a predecessor if there is no ordinal number beta such that beta+1=alpha.

A reflexive relation.

Pre-Calculus

Let A and B_j be sets. Conditional probability requires that P(A intersection B_j)=P(A)P(B_j|A), (1) where intersection denotes intersection ("and"), and also that P(A ...

A map is called bijective if it is both injective and surjective. A bijective map is also called a bijection. A function f admits an inverse f^(-1) (i.e., "f is invertible") ...

Every Boolean algebra is isomorphic to the Boolean algebra of sets. The theorem is equivalent to the maximal ideal theorem, which can be proved without using the axiom of ...

An axiomatic system is said to be categorical if there is only one essentially distinct representation for it. In particular, the names and types of objects within the system ...

The product of a family {X_i}_(i in I) of objects of a category is an object P=product_(i in I)X_i, together with a family of morphisms {p_i:P->X_i}_(i in I) such that for ...