Definition 0.1
A cohomological complex of topological vector spaces is a pair
where
is a sequence of topological vector spaces and
is
a sequence of continuous linear maps
from
into
which satisfy
.
Remarks
The dual complex of a cohomological complex
of topological vector spaces is the homological complex
, where
with
being the strong dual of
and
, and also with
being the transpose map of
.
A cohomological complex of topological vector spaces (TVS) is a
specific case of a cochain complex, which is the dual of the concept
of chain complex.
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