Discrete space

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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 is a uniform space 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.
  • Every map from a discrete space to a topological space is continuous.

References