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R^n is homeomorphic to R^m iff n=m. This theorem was first proved by Brouwer.

A notation invented by Dirac which is very useful in quantum mechanics. The notation defines the "ket" vector, denoted |psi>, and its conjugate transpose, called the "bra" ...

If (f,U) and (g,V) are functions elements, then (g,V) is a direct analytic continuation of (f,U) if U intersection V!=emptyset and f and g are equal on U intersection V.

The curve d(u) in the ruled surface parameterization x(u,v)=b(u)+vd(u).

If, in an interval of x, sum_(r=1)^(n)a_r(x) is uniformly bounded with respect to n and x, and {v_r} is a sequence of positive non-increasing quantities tending to zero, then ...

Two sets A_1 and A_2 are disjoint if their intersection A_1 intersection A_2=emptyset, where emptyset is the empty set. n sets A_1, A_2, ..., A_n are disjoint if A_i ...

A generalization by Kronecker of Kummer's theory of prime ideal factors. A divisor on a full subcategory C of mod(A) is an additive mapping chi on C with values in a ...

A number of attractive 11-compounds of the regular dodecahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

The "dot" · has several meanings in mathematics, including multiplication (a·b is pronounced "a times b"), computation of a dot product (a·b is pronounced "a dot b").

The symbol | which is not used very commonly in mathematics. The double dagger is also known as the double obelisk or diesis (Bringhurst 1997, p. 275).