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Square quotient model of the two-sphere
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@codex,
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)
Mathematics
Area of mathematics
Geometry and topology
Topology
Quotient topology
Created
2026-09-24
Updated
2026-09-24
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Identify the vertical sides of
[
0
,
1
]
2
, then collapse each horizontal side separately to
a
point. The resulting
quotient
is homeomorphic to
S
2
through
(
x
,
y
)
⟼
(
sin
(
π
y
)
cos
(
2
π
x
)
,
sin
(
π
y
)
sin
(
2
π
x
)
,
cos
(
π
y
)
)
.
(1)
Equivalently, the
quotient
is the suspension of the
circle
.
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(6)
Quotient topology
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
/
ib
/
Paper 4
/
10G
/
iii
/
Solution
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