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A module having dual properties with respect to a free module, as enumerated below. 1. Every free module is projective; every cofree module is injective. 2. For every module ...

The cup product is a product on cohomology classes. In the case of de Rham cohomology, a cohomology class can be represented by a closed form. The cup product of [alpha] and ...

A subset F subset R of the real numbers is said to be an F_sigma set provided F is the countable union of closed sets. The name F_sigma comes from French: The F stands for ...

If two intersections of each pair of three conics S_1, S_2, and S_3 lie on a conic S_0, then the lines joining the other two intersections of each pair are concurrent (Evelyn ...

A hexagonal prism is a prism composed of two hexagonal bases and six rectangular sides. It is an octahedron. The regular right hexagonal prism is a space-filling polyhedron. ...

A ket |psi> is a vector living in a dual vector space to that containing bras <psi|. Bras and kets are commonly encountered in quantum mechanics. Bras and kets can be ...

In the field of functional analysis, the Krein-Milman theorem is a result which characterizes all (nonempty) compact convex subsets K of "sufficiently nice" topological ...

The largest known prime numbers are Mersenne primes, the largest of these known as of September 2013 bing 2^(57885161)-1, which has a whopping 17425170 decimal digits. As of ...

The MacBeath circumconic is the dual conic to the MacBeath inconic, introduced in Dec. 2004 by P. Moses (Kimberling). It has circumconic parameters x:y:z=cosA:cosB:cosC, (1) ...

Suppose that A and B are two normed (Banach) algebras. A vector space X is called an A-B-bimodule whenever it is simultaneously a normed (Banach) left A-module, a normed ...