The Tietze Extension Theorem states that a continuous real-valued function defined on a closed subset of a normal topological space can always be extended to a continuous function on the whole space. Named for Heinrich Tietze, building on earlier work by Henri Lebesgue, it is a fundamental tool for constructing continuous functions with prescribed behavior on a subspace.
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StatementThe Tietze extension theorem states that any real valued continuous function defined on a closed subset of a normal topological space can be extended to a continuous function on the whole space, preserving boundedness if the original function was bounded. 1 Classification
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Source Heinrich Tietze (Wikipedia)
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Source Tietze Extension Theorem (Wikipedia)
Source Tietze Extension Theorem (Wikipedia)
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1. Tietze Extension Theorem (Wikipedia)
Wikimedia Foundationlead section, first paragraph
In topology, the Tietze extension theorem (also known as the Tietze-Urysohn-Brouwer extension theorem or Urysohn-Brouwer lemma) states that any real-valued, continuous function on a closed subset of a normal topological space can be extended to the entire space, preserving boundedness if necessary.
Proved By: Heinrich Tietze, Lead paragraph
In topology, the Tietze extension theorem (also known as the Tietze-Urysohn-Brouwer extension theorem or Urysohn-Brouwer lemma) states that any
Proved By: Pavel Urysohn, Lead paragraph
In topology, the Tietze extension theorem (also known as the Tietze-Urysohn-Brouwer extension theorem or Urysohn-Brouwer lemma) states that any real-valued, continuous function on a closed subset
In Group: General Topology, Lead paragraph
In topology, the Tietze extension theorem (also known as the Tietze-Urysohn-Brouwer extension theorem or Urysohn-Brouwer lemma) states that any real-valued, continuous function on a closed subset of a normal topological space can be extended to the entire space, preserving boundedness if necessary.
View the Source Heinrich Tietze (Wikipedia)
Principal Result Of: Heinrich Tietze, Article textQuote, Principal Result Of: Heinrich Tietze, Article text
Heinrich Franz Friedrich Tietze (August 31, 1880, February 17, 1964) was an Austrian mathematician, famous for the Tietze extension theorem on functions from topological spaces to the real numbers.
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