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A noncompact manifold without boundary.

A map which sends open sets to open sets.

In a topological space X, an open neighborhood of a point x is an open set containing x. A set containing an open neighborhood is simply called a neighborhood.

The theory and applications of Laplace transforms and other integral transforms.

Let A:D(A)->H and B:D(B)->H be linear operators from domains D(A) and D(B), respectively, into a Hilbert space H. It is said that B extends A if D(A) subset D(B) and if Bv=Av ...

A broad area of mathematics connected with functional analysis, differential equations, index theory, representation theory, and mathematical physics.

Given an acute angle in a right triangle, the opposite side is the leg of the triangle which is not incident on the angle. Lengths of opposite and adjacent sides appear ...

A topology defined on a totally ordered set X whose open sets are all the finite intersections of subsets of the form {x in X|x>a} or {x in X|x<a}, where a in X. The order ...

A pair of quantities (a, b) where ordering is significant, so (a, b) is considered distinct from (b, a) for a!=b.

An ambiguous term which is sometimes used to mean a partially ordered set and sometimes to mean a totally ordered set.