Indiscrete space: Difference between revisions

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In [[topology]], an '''indiscrete space''' is a [[topological space]] with the '''indiscrete topology''', in which the only open [[subset]]s are the empty subset and the space itself.
==Properties==
* An indiscrete space is [[metric space|metrizable]] if and only if it has at most one point
* An indiscrete space is [[compact space|compact]].
* An indiscrete space is [[connected space|connected]].
* Every map from a topological space to an indiscrete space is [[continuous map|continuous]].
==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 }}

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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