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Pavel Samuilovich Urysohn (in Russian: Па́вел Самуи́лович Урысо́н; 3 February, 1898 – 17 August, 1924) was a
Soviet mathematician who is best
known for...
- 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...
- In topology, a
discipline within mathematics, an
Urysohn space, or T2½ space, is a
topological space in
which any two
distinct points can be separated...
- the
Tietze extension theorem (also
known as the Tietze–
Urysohn–Brouwer
extension theorem or
Urysohn-Brouwer lemma)
states that any real-valued, continuous...
- In the
field of topology, a Fréchet–
Urysohn space is a
topological space X{\displaystyle X} with the
property that for
every subset S⊆X{\displaystyle...
- homeomorphic. One of the
first widely recognized metrization theorems was
Urysohn's metrization theorem. This
states that
every Hausdorff second-countable...
-
sequential coreflection of X.{\displaystyle X.} The
related concepts of Fréchet–
Urysohn spaces, T-sequential spaces, and N{\displaystyle N}-sequential
spaces are...
-
usage is
still not consistent.
Steen and
Seebach define a
Urysohn space as "a
space with a
Urysohn function for any two points".
Willard calls this a completely...
- x.} A
space with this
sequence property is
sometimes called a Fréchet–
Urysohn space. First-countability is
strictly weaker than second-countability....
- X=0} if and only if IndX=0.{\displaystyle \operatorname {Ind} X=0.}
Urysohn's theorem states that when X is a
normal space with a
countable base, then...
