- 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.
- Lynn Arthur Steen; J. Arthur Seebach jr (1978). Counterexamples in Topology. Berlin, New York: Springer-Verlag, 41-42. ISBN 0-387-90312-7.
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