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Continuous Linear Transformation Types Of Homomorphisms Sequence Chain Complex Cohomological Complex Of Topological Vector Spaces
| 1 | Types Of Homomorphisms |
| 1 | Linear Transformation |
| 1 | Continuous |
| 1 | Sequence |
| 4 | Chain Complex |
| 10 | Cohomological Complex Of Topological Vector Spaces |
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Homological Complex Of Topological Vector Spaces
Definition 0.1
A homological 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
.
,
where
is a sequence of topological vector spaces
and
is a sequence
of continuous
linear maps
from
into which satisfy
.Remarks
- The homological complex of topological vector spaces is a specifc example of a chain complex.
- A sequence of
-modules and their homomorphisms
is said to be a 
-complex.