Further examples Compactifications of discrete spaces The one-point compactification of the set of positive integers is homeomorphic to the space consisting of K = {0} U {1/n | n is a positive integer} with the order topology. A sequence in a topological space converges to a point in , if and only if the map given by for in and is continuous. Here has the discrete topology. Polyadic spaces 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.
Further examples Compactifications of discrete spaces The one-point compactification of the set of positive integers is homeomorphic to the space consisting of K = {0} U {1/n | n is a positive integer} with the order topology. A sequence in a topological space converges to a point in  if and only if the map given by for in and is continuous Here has the discrete topology. Polyadic spaces 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