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Miklós Schweitzer
2006 Miklós Schweitzer
9
9
Part of
2006 Miklós Schweitzer
Problems
(1)
self homeomorphism of circle
Source: miklos schweitzer 2006 q9
9/3/2021
Does the circle T = R / Z have a self-homeomorphism
ϕ
\phi
ϕ
that is singular (that is, its derivative is almost everywhere 0), but the mapping
f
:
T
→
T
f:T \to T
f
:
T
→
T
,
f
(
x
)
=
ϕ
−
1
(
2
ϕ
(
x
)
)
f(x) = \phi^{-1} (2\phi(x))
f
(
x
)
=
ϕ
−
1
(
2
ϕ
(
x
))
is absolutely continuous?
topology
homeomorphism
absolute continuity