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

The complex plane C with the origin removed, i.e., C-{0}. The punctured plane is sometimes denoted C^* (although this notation conflicts with that for the Riemann sphere C-*, ...

A Reeb component is a Reeb foliation (M,F) whose leaves are proper. A foliation which has no Reeb components is said to be Reebless.

Given any two distinct points x,y, there exist neighborhoods u and v of x and y, respectively, with u intersection v=emptyset. It then follows that finite subsets are closed.

One of Cantor's ordinal numbers omega, omega+1, omega+2, ..., omega+omega, omega+omega+1, ... which is "larger" than any whole number.

Dynamical Systems

The map H_n(X,A)->H_(n-1)(A) appearing in the long exact sequence of a pair axiom.

A topological space.

A field of extremals is a plane region which is simply connected by a one-parameter family of extremals. The concept was invented by Weierstrass.

A property of a space which is also true of each of its subspaces. Being "first-countable" is hereditary, but having a given genus is not.