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Two totally ordered sets (A,<=) and (B,<=) are order isomorphic iff there is a bijection f from A to B such that for all a_1,a_2 in A, a_1<=a_2 iff f(a_1)<=f(a_2) (Ciesielski ...

Let X=(X,tau) be a topological vector space whose continuous dual X^* may or may not separate points (i.e., may or may not be T2). The weak-* (pronounced "weak star") ...

Let X=(X,tau) be a topological vector space whose continuous dual X^* separates points (i.e., is T2). The weak topology tau_w on X is defined to be the coarsest/weakest ...

A discontinuity is point at which a mathematical object is discontinuous. The left figure above illustrates a discontinuity in a one-variable function while the right figure ...

The terms "measure," "measurable," etc. have very precise technical definitions (usually involving sigma-algebras) that can make them appear difficult to understand. However, ...

The resolution principle, due to Robinson (1965), is a method of theorem proving that proceeds by constructing refutation proofs, i.e., proofs by contradiction. This method ...

An abstract simplicial complex is a collection S of finite nonempty sets such that if A is an element of S, then so is every nonempty subset of A (Munkres 1993, p. 15).

An additive category is a category for which the morphism sets have the structure of Abelian groups. It satisfies some, but not all the properties of an Abelian category.

A technical mathematical object which bears the same resemblance to binary relations as categories do to functions and sets.

The process used to generate an expression for a covariant in the first degree of any one of the equivalent sets of coefficients for a curve.