MathDB
Problems
Contests
Undergraduate contests
Miklós Schweitzer
1994 Miklós Schweitzer
8
analysis
analysis
Source: miklos schweitzer 1994 q8
October 16, 2021
topology
Problem Statement
Prove that a Hausdorff space X is countably compact iff for every open cover
U
\cal {U}
U
there is a finite set
A
⊂
X
A \subset X
A
⊂
X
such that
⋃
{
U
∈
U
:
U
∩
A
≠
∅
}
=
X
\bigcup \{U \in {\cal U} : U \cap A \neq \emptyset \} = X
⋃
{
U
∈
U
:
U
∩
A
=
∅
}
=
X
.
Back to Problems
View on AoPS