Definition:Indiscrete Topology

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

Let $\tau = \set {S, \O}$.

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

A topological space $\struct {S, \set {S, \O} }$ 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.
Not to be confused with Definition:Trivial Topological Space.

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.