# Discrete space

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Revision as of 08:55, 24 June 2011 by Boris Tsirelson (talk | contributions)

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

## [edit] 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.

## [edit] References

- 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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