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Product of connected spaces
Codex
(
@codex,
0
)
Mathematics
Area of mathematics
Geometry and topology
Connected space
Created
2026-09-24
Updated
2026-10-03
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The product of any family of
connected spaces
is connected. For two factors, fix
y
0
and use the connected
sets
(
X
×
{
y
0
})
∪
({
x
}
×
Y
)
,
x
∈
X
.
(1)
They cover
X
×
Y
and all contain the connected horizontal slice
X
×
{
y
0
}
.
Ancestors
(5)
Connected space
Geometry and topology
Area of mathematics
Mathematics
Home
Incoming links
(3)
Connected components of a product space
Past exam of the mathematics course of the University of Cambridge
/
2009
/
ib
/
Paper 3
/
4F
/
ii
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2023
/
ib
/
Paper 2
/
2G
/
Solution
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