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In an exterior algebra ^ V, a top-dimensional form has degree n where n=dimV. Any form of higher degree must be zero. For example, if V=R^4 then alpha=e_1 ^ e_2 ^ e_3 ^ e_4 ...

A product involving an infinite number of terms. Such products can converge. In fact, for positive a_n, the product product_(n=1)^(infty)a_n converges to a nonzero number iff ...

The term "higher dimensional group theory" was introduced by Brown (1982), and refers to a method for obtaining new homotopical information by generalizing to higher ...

At the age of 17, Bernard Mares proposed the definite integral (Borwein and Bailey 2003, p. 26; Bailey et al. 2006) C_2 = int_0^inftycos(2x)product_(n=1)^(infty)cos(x/n)dx ...

The Lebesgue covering dimension is an important dimension and one of the first dimensions investigated. It is defined in terms of covering sets, and is therefore also called ...

Informally, self-similar objects with parameters N and s are described by a power law such as N=s^d, where d=(lnN)/(lns) is the "dimension" of the scaling law, known as the ...

Each centered convex body of sufficiently high dimension has an "almost spherical" k-dimensional central section.

A linear transformation between two vector spaces V and W is a map T:V->W such that the following hold: 1. T(v_1+v_2)=T(v_1)+T(v_2) for any vectors v_1 and v_2 in V, and 2. ...

The dimension of an object is a topological measure of the size of its covering properties. Roughly speaking, it is the number of coordinates needed to specify a point on the ...

An extension field F subset= K is called finite if the dimension of K as a vector space over F (the so-called degree of K over F) is finite. A finite field extension is ...