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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 ...

If the trilinear polars of the polygon vertices of a triangle are distinct from the respectively opposite sides, they meet the sides in three collinear points.

The Christoffel symbols are tensor-like objects derived from a Riemannian metric g. They are used to study the geometry of the metric and appear, for example, in the geodesic ...

The number of ways to arrange n distinct objects along a fixed (i.e., cannot be picked up out of the plane and turned over) circle is P_n=(n-1)!. The number is (n-1)! instead ...

A linear operator A:D(A)->H from its domain D(A) into a Hilbert space H is closable if it has a closed extension B:D(B)->H where D(A) subset D(B). Closable operators are ...

Codimension is a term used in a number of algebraic and geometric contexts to indicate the difference between the dimension of certain objects and the dimension of a smaller ...

A partially ordered set (or ordered set or poset for short) (L,<=) is called a complete lattice if every subset M of L has a least upper bound (supremum, supM) and a greatest ...

Let P be the principal (initial investment), r be the annual compounded rate, i^((n)) the "nominal rate," n be the number of times interest is compounded per year (i.e., the ...

Let X and Y be sets, and let R subset= X×Y be a relation on X×Y. Then R is a concurrent relation if and only if for any finite subset F of X, there exists a single element p ...

The following conditions are equivalent for a conservative vector field on a particular domain D: 1. For any oriented simple closed curve C, the line integral ∮_CF·ds=0. 2. ...