one-point compactification

one-point compactification

[′wən ‚pȯint kəm‚pak·tə·fə′kā·shən]
(mathematics)
The one-point compactification of a topological space X is the union of X with a set consisting of a single element, with the topology of consisting of the open subsets of X and all subsets of whose complements in are closed compact subsets in X. Also known as Alexandroff compactification.
References in periodicals archive ?
The stereographic projection (20) identifies [S.sup.2] with the one-point compactification of the [zeta]-plane.
Let X be the one-point compactification of the space Y and denote by p the unique point of the set X\Y.
Not unlike the one-point compactification of the complex plane by adding the points at infinity leading to the Gauss-Riemann sphere.