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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.

The illusion illustrated above in which the bounding rectangle and inner square both appear distorted.

A tree is planted at each lattice point in a circular orchard which has center at the origin and radius r. If the radius of trees exceeds 1/r units, one is unable to see out ...

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.