Discrete space

In topology, a discrete space is a topological space with the discrete topology, in which every subset is open.

Properties

 * A discrete space is metrizable, with the topology induced by the discrete metric.
 * A discrete space can be turned into a uniform space, being endowed with the discrete uniformity.
 * A discrete space is compact if and only if it is finite.
 * A discrete space is connected if and only if it has at most one point.