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Fibre bijection by path lifting
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Area of mathematics
Geometry and topology
Algebraic topology
Covering space
Classification of connected covering spaces
Degree of a connected covering
Created
2026-09-24
Updated
2026-09-24
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If the base of
a
covering is path-connected,
a
path from
x
0
to
x
1
gives
a
bijection
p
−
1
(
x
0
)
⟶
p
−
1
(
x
1
)
(1)
by sending each initial lift point to the endpoint of its unique lifted path. Lifting the reversed path gives the inverse
bijection
.
Ancestors
(8)
Degree of a connected covering
Classification of connected covering spaces
Covering space
Algebraic topology
Geometry and topology
Area of mathematics
Mathematics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2023
/
ii
/
Paper 2
/
21G
/
Solution
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