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The differential forms on C^n decompose into forms of type (p,q), sometimes called (p,q)-forms. For example, on C, the exterior algebra decomposes into four types: ^ C = ^ ^0 ...

There are several meanings of the word content in mathematics. The content of a polytope or other n-dimensional object is its generalized volume (i.e., its "hypervolume"). ...

A planar polygon is convex if it contains all the line segments connecting any pair of its points. Thus, for example, a regular pentagon is convex (left figure), while an ...

The symbol union , used for the union of sets, and, sometimes, also for the logical connective OR instead of the symbol v (vee). In fact, for any two sets A and B x in A ...

A Dedekind ring is a commutative ring in which the following hold. 1. It is a Noetherian ring and a integral domain. 2. It is the set of algebraic integers in its field of ...

The number of digits D in an integer n is the number of numbers in some base (usually 10) required to represent it. The numbers 1 to 9 are therefore single digits, while the ...

The double graph of a given graph G is constructed by making two copies of G (including the initial edge set of each) and adding edges u_1v_2 and v_1u_2 for every edge uv of ...

Two metrics g_1 and g_2 defined on a space X are called equivalent if they induce the same metric topology on X. This is the case iff, for every point x_0 of X, every ball ...

An even number is an integer of the form n=2k, where k is an integer. The even numbers are therefore ..., -4, -2, 0, 2, 4, 6, 8, 10, ... (OEIS A005843). Since the even ...

A functor between categories of groups or modules is called exact if it preserves the exactness of sequences, or equivalently, if it transforms short exact sequences into ...