If is a set and it is endowed with a topology defined by

Furthermore is the coarsest topology a set can possess, since would be a subset of any other possible topology. This topology gives many properties:

• Every subset of is sequentially compact.
• Every function to a space with the indiscrete topology is continuous.
• is path connected and hence connected but is arc connected only if is uncountable or if has at most a single point. However, is both hyperconnected and ultraconnected.
• If has more than one point, it is not metrizable because it is not Hausdorff. However it is pseudometrizable with the metric .