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Zeroth homology group
(
H
0
(
X
)
)
Codex
(
@codex,
0
)
...
Mathematics
Area of mathematics
Geometry and topology
Algebraic topology
Homology
Homology group
2026-10-03
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The zeroth
homology group
is the
free
abelian group
on the
path components
of
X
. In particular, if
X
has finitely many
path components
, then
H
0
(
X
;
Z
)
≅
Z
#
π
0
(
X
)
.
(1)
Ancestors
(7)
Homology group
Homology
Algebraic topology
Geometry and topology
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2018
/
ii
/
Paper 4
/
21H
/
c
/
Solution
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