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Square quotient model of the two-sphere
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Quotient topology
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Words: 41
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
)
)
.
(126)
Equivalently, the quotient is the suspension of the circle.
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Quotient topology
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