Subspace topology: Difference between revisions

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==References==
==References==
* {{cite book | author=Wolfgang Franz | title=General Topology | publisher=Harrap | year=1967 | pages=36 }}
* {{cite book | author=Wolfgang Franz | title=General Topology | publisher=Harrap | year=1967 | pages=36 }}
* {{cite book | author=J.L. Kelley | authorlink=John L. Kelley | title=General topology | publisher=van Nostrand | year= 1955 | pages=50-53 }}
* {{cite book | author=J.L. Kelley | authorlink=John L. Kelley | title=General topology | publisher=van Nostrand | year= 1955 | pages=50-53 }}[[Category:Suggestion Bot Tag]]

Latest revision as of 07:01, 23 October 2024

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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.