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.
Title  homological complex of topological vector spaces 
Canonical name  HomologicalComplexOfTopologicalVectorSpaces 
Date of creation  20130322 18:17:24 
Last modified on  20130322 18:17:24 
Owner  bci1 (20947) 
Last modified by  bci1 (20947) 
Numerical id  15 
Author  bci1 (20947) 
Entry type  Definition 
Classification  msc 55N25 
Classification  msc 55N99 
Classification  msc 55R65 
Classification  msc 55P99 
Synonym  ChainComplex 
Related topic  ChainComplex 
Related topic  CategoricalSequence 
Related topic  ExactSequence 
Related topic  TangentialCauchyRiemannComplexOfCinftySmoothForms 
Related topic  HomolgyOfMathbbRP3 
Related topic  CohomologicalComplexOfTopologicalVectorSpaces 
Related topic  ACRcomplex 
Defines  homological complex of topological vector spaces 