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The homomorphism S which, according to the snake lemma, permits construction of an exact sequence (1) from the above commutative diagram with exact rows. The homomorphism S ...

Pairs of primes of the form (p, p+4) are called cousin primes. The first few are (3, 7), (7, 11), (13, 17), (19, 23), (37, 41), (43, 47), (67, 71), ... (OEIS A023200 and ...

The direct product is defined for a number of classes of algebraic objects, including sets, groups, rings, and modules. In each case, the direct product of an algebraic ...

An embedding is a representation of a topological object, manifold, graph, field, etc. in a certain space in such a way that its connectivity or algebraic properties are ...

A diagram lemma which states that, given the commutative diagram of additive Abelian groups with exact rows, the following holds: 1. If f_0 is surjective, and f_1 and f_3 are ...

Let C^*(u) denote the number of nowhere-zero u-flows on a connected graph G with vertex count n, edge count m, and connected component count c. This quantity is called the ...

There are three types of so-called fundamental forms. The most important are the first and second (since the third can be expressed in terms of these). The fundamental forms ...

Given a compact manifold M and a transversely orientable codimension-one foliation F on M which is tangent to partialM, the pair (M,F) is called a generalized Reeb component ...

Two mathematical objects are said to be homotopic if one can be continuously deformed into the other. For example, the real line is homotopic to a single point, as is any ...

An interval is a connected portion of the real line. If the endpoints a and b are finite and are included, the interval is called closed and is denoted [a,b]. If the ...