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...

local lemma Nakayama's lemma Poincaré's lemma Riesz's lemma Schur's lemma Schwarz's lemma Sperner's lemma Urysohn's lemma Vitali covering lemma Yoneda's...

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...

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...

cohomology Invariance of domain Poincaré conjecture Tychonoff's theorem Urysohn's lemma Category Mathematics portal Wikibook Wikiversity Topics general algebraic...

theorem (to do) Ultrafilter lemma Ultraparallel theorem Urysohn's lemma Van der Waerden's theorem Wilson's theorem Zorn's lemma Bellman–Ford algorithm (to...