Discrete metric: Difference between revisions
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The '''discrete metric''' on a set is an example of a [[metric]]. | The '''discrete metric''' on a set is an example of a [[metric]]. | ||
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==Properties== | ==Properties== | ||
* A discrete metric space is [[ | * A discrete metric space is [[complete metric space|complete]] | ||
* The [[topological space|topology]] induced by the discrete metric is the discrete topology, in which every set is open. | * The [[topological space|topology]] induced by the discrete metric is the [[discrete space|discrete topology]], in which every set is open. | ||
Latest revision as of 12:47, 4 January 2009
The discrete metric on a set is an example of a metric.
Definition
The discrete metric d on a set X is defined by
Properties
- A discrete metric space is complete
- The topology induced by the discrete metric is the discrete topology, in which every set is open.