45
Sign In
Sign Up
English
Français
العربية
Deutsch
🏠
/
Mathematics
/
Topology
/
Urysohn's Lemma
Urysohn's Lemma
📜
The statement of the theorem
In a normal topological space, for any two disjoint closed sets
A
A
A
and
B
B
B
, there exists a continuous function
f
f
f
mapping the space to
[
0
,
1
]
[0, 1]
[
0
,
1
]
such that
f
(
A
)
=
0
f(A) = \\{0\\}
f
(
A
)
=
0
and
f
(
B
)
=
1
f(B) = \\{1\\}
f
(
B
)
=
1
.
Source: Wikipedia