Math 2.0

General topology Standard examples of topologies Example

Indiscrete topology

Example

Let XX be a set and let τ={∅,X}\tau = \{\varnothing, X\}. Then τ\tau is a topology on XX, the indiscrete topology, also called the trivial topology.

Remarks

It is the coarsest topology on XX. Each function from any topological space to an indiscrete space is continuous. In an indiscrete space, each sequence converges to each point. Thus, if XX has at least two points, the space is not Hausdorff and not metrizable. Each indiscrete space is compact and connected.

Further reading

  1. Web https://en.wikipedia.org/wiki/Trivial_topology, lead section
  2. Web https://en.wikipedia.org/wiki/Trivial_topology, Details
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