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A topological groupoid over B is a groupoid G such that B and G are topological spaces and alpha,beta, and multiplication are continuous maps. Here, alpha and beta are maps ...

A topological partial algebra is a pair (A,tau), where A=(A,(f_i^A)_(i in I)) is a partial algebra and each of the operations f_i^A is continuous in the product topology. ...

The probability law on the space of continuous functions g with g(0)=0, induced by the Wiener process.

Let f(x) be a real continuous monotonic strictly increasing function on the interval [0,a] with f(0)=0 and b<=f(a), then ab<=int_0^af(x)dx+int_0^bf^(-1)(y)dy, where f^(-1)(y) ...

If f is a function on an open set U, then the zero set of f is the set Z={z in U:f(z)=0}. A subset of a topological space X is called a zero set if it is equal to f^(-1)(0) ...

Differential Geometry

The objective of global optimization is to find the globally best solution of (possibly nonlinear) models, in the (possible or known) presence of multiple local optima. ...

The Banach-Steinhaus theorem is a result in the field of functional analysis which relates the "size" of a certain subset of points defined relative to a family of linear ...

The Cantor function F(x) is the continuous but not absolutely continuous function on [0,1] which may be defined as follows. First, express x in ternary. If the resulting ...

A category consists of three things: a collection of objects, for each pair of objects a collection of morphisms (sometimes call "arrows") from one to another, and a binary ...