Subspace topology

From Citizendium
Jump to navigation Jump to search
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 general topology, the subspace topology, or induced or relative topology, is the assignment of open sets to a subset of a topological space.

Let (X,T) be a topological space with T the family of open sets, and let A be a subset of X. The subspace topology on A is the family

The subspace topology makes the inclusion map AX continuous and is the coarsest topology with that property.

References

  • Wolfgang Franz (1967). General Topology. Harrap, 36. 
  • J.L. Kelley (1955). General topology. van Nostrand, 50-53.