Topological space

Discrete topology

On any set the discrete topology of is one where all subsets of are considered open (and therefore also closed, since the compliment of any subset is necessarily also a subset and therefore open), i.e. . Such a topology is the finest topology that can be formed on any set.

Metric

A discrete topology is metrizable with the so-called discrete metric

although there may exist other metricisations.

Properties

• A topological space is discrete iff every point is its own connected component

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