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homological complex of topological vector spaces
Definition 0.1.
A homological 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 $E_{{q+1}}$ into $E_{q}$ which satisfy $d_{q}\circ d_{{q+1}}=0$.
Remarks

The homological complex of topological vector spaces is a specifc example of a chain complex.

A sequence of $R$modules and their homomorphisms is said to be a $R$complex.
Defines:
homological complex of topological vector spaces
Keywords:
homological complex, topological vector spaces, homological complex of topological vector spaces
Related:
ChainComplex, CategoricalSequence, ExactSequence,TangentialCauchyRiemannComplexOfCinftySmoothForms, HomolgyOfMathbbRP3, CohomologicalComplexOfTopologicalVectorSpaces, ACRcomplex
Synonym:
ChainComplex
Type of Math Object:
Definition
Major Section:
Reference
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