Discrete space: Difference between revisions

From Citizendium
Jump to navigation Jump to search
imported>Richard Pinch
(Every map from a discrete space to a topological space is continuous)
mNo edit summary
 
Line 10: Line 10:


==References==
==References==
* {{cite book | author=Lynn Arthur Steen | authorlink=Lynn Arthur Steen | coauthors= J. Arthur Seebach jr | title=[[Counterexamples in Topology]] | year=1978 | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=0-387-90312-7 | pages=41-42 }}
* {{cite book | author=Lynn Arthur Steen | authorlink=Lynn Arthur Steen | coauthors= J. Arthur Seebach jr | title=[[Counterexamples in Topology]] | year=1978 | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=0-387-90312-7 | pages=41-42 }}[[Category:Suggestion Bot Tag]]

Latest revision as of 17:00, 7 August 2024

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

In topology, a discrete space is a topological space with the discrete topology, in which every subset is open.

Properties

  • A discrete space is metrizable, with the topology induced by the discrete metric.
  • A discrete space is a uniform space with the discrete uniformity.
  • A discrete space is compact if and only if it is finite.
  • A discrete space is connected if and only if it has at most one point.
  • Every map from a discrete space to a topological space is continuous.

References