Editing Alexandroff extension (section)

=== Compactifications of discrete spaces===
* The one-point compactification of the set of positive integers is [[Homeomorphism|homeomorphic]] to the space consisting of ''K'' = {0} U {1/''n'' | ''n'' is a positive integer} with the order topology.
* A sequence <math>\{a_n\}</math> in a topological space <math>X</math> converges to a point <math>a</math> in <math>X</math>, if and only if the map <math>f\colon\mathbb N^*\to X</math> given by <math>f(n) = a_n</math> for <math>n</math> in <math>\mathbb N</math> and <math>f(\infty) = a</math> is continuous. Here <math>\mathbb N</math> has the [[discrete topology]].
* [[Polyadic space]]s are defined as topological spaces that are the continuous image of the power of a one-point compactification of a discrete, locally compact Hausdorff space.