In topology, Urysohn's lemma is a lemma that states that a topological space is normal if and only if any two disjoint closed subsets can be separated...
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contributions in dimension theory, and for developing Urysohn's metrization theorem and Urysohn's lemma, both of which are fundamental results in topology...
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Poincaré's lemma Riesz's lemma Schur's lemma Schwarz's lemma Sperner's lemma Urysohn's lemma Vitali covering lemma Yoneda's lemma Zorn's lemma While these...
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Tietze extension theorem (redirect from Urysohn-Brouwer lemma)
Tietze extension theorem (also known as the Tietze–Urysohn–Brouwer extension theorem or Urysohn-Brouwer lemma) states that any real-valued, continuous function...
9 KB (1,673 words) - 00:29, 31 July 2024
f^{-1}(1)=F} . This is a stronger separation property than normality, as by Urysohn's lemma disjoint closed sets in a normal space can be separated by a function...
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regular. Compact preregular spaces are normal, meaning that they satisfy Urysohn's lemma and the Tietze extension theorem and have partitions of unity subordinate...
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disjoint closed sets can be separated by a continuous function; this is Urysohn's lemma.) X is completely normal, or T5 or completely T4, if it is T1 and if...
42 KB (5,724 words) - 02:31, 8 November 2023
Completely Hausdorff space Regular space Tychonoff space Normal space Urysohn's lemma Tietze extension theorem Paracompact Separated sets Direct sum and...
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continuity lemma Lindelöf's lemma Urysohn's lemma Tube lemma Morse lemma Knaster–Kuratowski–Mazurkiewicz lemma Dehn's lemma Ellis–Numakura lemma (topological...
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perhaps the single most important result in general topology (along with Urysohn's lemma). The theorem is also valid for topological spaces based on fuzzy sets...
15 KB (2,094 words) - 09:49, 19 July 2024