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IMS
2007 IMS
8
8
Part of
2007 IMS
Problems
(1)
Fixed point
Source: IMS 2007
5/18/2007
Let
T
=
{
(
t
q
,
1
−
t
)
∈
R
2
∣
t
∈
[
0
,
1
]
,
q
∈
Q
}
T=\{(tq,1-t) \in\mathbb R^{2}| t \in [0,1],q\in\mathbb Q\}
T
=
{(
tq
,
1
−
t
)
∈
R
2
∣
t
∈
[
0
,
1
]
,
q
∈
Q
}
Prove that each continuous function
f
:
T
⟶
T
f: T\longrightarrow T
f
:
T
⟶
T
has a fixed point.
function
topology
real analysis
real analysis unsolved