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...

contributions in dimension theory, and for developing Urysohn's metrization theorem and Urysohn's lemma, both of which are fundamental results in topology...

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...

Tietze extension theorem (also known as the Tietze–Urysohn–Brouwer extension theorem or Urysohn-Brouwer lemma) states that any real-valued, continuous function...

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...

regular. Compact preregular spaces are normal, meaning that they satisfy Urysohn's lemma and the Tietze extension theorem and have partitions of unity subordinate...

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...

Completely Hausdorff space Regular space Tychonoff space Normal space Urysohn's lemma Tietze extension theorem Paracompact Separated sets Direct sum and...

continuity lemma Lindelöf's lemma Urysohn's lemma Tube lemma Morse lemma Knaster–Kuratowski–Mazurkiewicz lemma Dehn's lemma Ellis–Numakura lemma (topological...

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...