cohomological complex

Definition 0.1   A cohomological complex of topological vector spaces is a pair $ (E^{\bullet}, d)$ where $ (E^{\bullet} = (E^q)_{q \in Z} $ is a sequence of topological vector spaces and $ d = (d^q)_{q \in Z }$ is a sequence of continuous linear maps $ d^q$ from $ E^{q}$ into $ E^{q+1}$ which satisfy $ d^q \circ d^{q+1} = 0$ .

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