Indiscrete space: Difference between revisions

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==References==
==References==
* {{cite book | author=Lynn Arthur Steen | authorlink=Lynn Arthur Steen | coauthors= J. Arthur Seebach jr | title=[[Counterexamples in Topology]] | year=1978 | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=0-387-90312-7 }}
* {{cite book | author=Lynn Arthur Steen | authorlink=Lynn Arthur Steen | coauthors= J. Arthur Seebach jr | title=[[Counterexamples in Topology]] | year=1978 | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=0-387-90312-7 }}[[Category:Suggestion Bot Tag]]

Latest revision as of 17:00, 31 August 2024

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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.

Properties

  • 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.

References