Definition:Indiscrete Topology

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Definition

Let $S \ne \varnothing$ be a set.

Let $\tau = \left\{{S, \varnothing}\right\}$.


Then $\tau$ is called the indiscrete topology on $S$.


A topological space $\left({S, \left\{{S, \varnothing}\right\}}\right)$ is known as an indiscrete space.


Also known as

  • The trivial topology (on $S$)
  • The nondiscrete topology (on $S$)


Also see

  • Results about indiscrete topologies can be found here.


Linguistic Note

Be careful how you spell indiscrete. A common homophone horror is to refer to this as the indiscreet topology.

However, indiscreet means incautious or tactless. It's how you describe somebody who cannot keep a secret.


Sources