MathDB
Problems
Contests
Undergraduate contests
Putnam
1968 Putnam
B6
B6
Part of
1968 Putnam
Problems
(1)
Putnam 1968 B6
Source: Putnam 1968
2/19/2022
Show that one cannot find compact sets
A
1
,
A
2
,
A
3
,
…
A_1, A_2, A_3, \ldots
A
1
,
A
2
,
A
3
,
…
in
R
\mathbb{R}
R
such that (1) All elements of
A
n
A_n
A
n
are rational. (2) Any compact set
K
⊂
R
K\subset \mathbb{R}
K
⊂
R
which only contains rational numbers is contained in some
A
m
A_{m}
A
m
.
Putnam
topology
compact set
college contests
real analysis