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If P is any point on a line TT^' whose orthopole is S, then the circle power of S with respect to the pedal circle of P is a constant (Gallatly 1913, p. 51).

A letter is an element of an alphabet. A collection of letters forms a word.

A Lie groupoid over B is a groupoid G for which G and B are differentiable manifolds and alpha,beta and multiplication are differentiable maps. Furthermore, the derivatives ...

Given a map f from a space X to a space Y and another map g from a space Z to a space Y, does there exist a map h from X to Z such that gh=f? If such a map h exists, then h ...

A line bundle is a special case of a vector bundle in which the fiber is either R, in the case of a real line bundle, or C, in the case of a complex line bundle.

A linear functional on a real vector space V is a function T:V->R, which satisfies the following properties. 1. T(v+w)=T(v)+T(w), and 2. T(alphav)=alphaT(v). When V is a ...

A subset M of a Hilbert space H is a linear manifold if it is closed under addition of vectors and scalar multiplication.

A function f such that |f(x)-f(y)|<=C|x-y| for all x and y, where C is a constant independent of x and y, is called a Lipschitz function. For example, any function with a ...

Let X be a topological vector space and for an arbitrary point x in X, denote by N_(x) the collection of all neighborhoods of x in X. A local base at x is any set B subset ...

A topological space is locally connected at the point x if every neighborhood of x contains a connected open neighborhood. It is called locally connected if it is locally ...