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2007 IMS
8
Fixed point
Fixed point
Source: IMS 2007
May 18, 2007
function
topology
real analysis
real analysis unsolved
Problem Statement
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.
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