Indiscrete space

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In topology, an indiscrete space is a topological space with the indiscrete topology, in which the only open subsets are the empty subset and the space itself.


  • An indiscrete space is metrizable if and only if it has at most one point
  • An indiscrete space is compact.
  • An indiscrete space is connected.
  • Every map from a topological space to an indiscrete space is continuous.