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.  
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==
==Properties==

Revision as of 16:04, 4 January 2013

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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