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{title2=$\check H^p(\mathcal U,\mathcal F)$}
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For an open cover $\mathcal U=(U_i)$, the Čech cochain group is
$$
\check C^p(\mathcal U,\mathcal F)=\prod_{i_0<\cdots<i_p}\mathcal F(U_{i_0}\cap\cdots\cap U_{i_p}),
$$
with the alternating sum of restrictions as differential. Its cohomology is the Čech cohomology of $\mathcal F$ with respect to $\mathcal U$.


Čech cohomology

{wiki=Čech_cohomology}

Čech cohomology is a mathematical tool used in algebraic topology to study the properties of topological spaces. Named after the Czech mathematician Eduard Čech, this cohomology theory is particularly useful for analyzing spaces that may not be well-behaved in a classical sense.


 Čech cohomology

ID: cech-cohomology