位相幾何学 - 暇つぶし2ch

位相幾何学 at MATH

264:１３２人目の素数さん
03/09/14 20:34
>>263
Googleで"Cech homology"を検索しろ。

例えば：
Cech homology
An entirely different way of finding a simplicial complex
in a topological space is by taking an open cover
and letting a simplex be a subset of the cover
with nonempty intersection. This simplicial complex
is called the nerve of the cover. For each cover
we obtain a homology group. Given a cover and a refinement,
we can map the simplices belonging to the refinement
to simplices belonging to the first cover by picking
for each open set in the refinement a member of
the first cover containing it.
This leads to a homomorphism of homology groups.
The collection of all open covers is directed
for refinement, and we get an inverse system.
The inverse limit is the Cech homology group.

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