Discrete metric: Difference between revisions

From Citizendium
Jump to navigation Jump to search
imported>Richard Pinch
(new entry, just a stub)
 
mNo edit summary
 
(3 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{subpages}}
The '''discrete metric''' on a set is an example of a [[metric]].
The '''discrete metric''' on a set is an example of a [[metric]].


Line 8: Line 9:


==Properties==
==Properties==
* A discrete metric space is [[completeness (mathematics)|complete]]
* 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.[[Category:Suggestion Bot Tag]]

Latest revision as of 16:00, 7 August 2024

This article is a stub and thus not approved.
Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
This editable Main Article is under development and subject to a disclaimer.

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