cohomological complex of topological vector spaces
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 (http://planetmath.org/HomologicalComplexOfTopologicalVectorSpaces), 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.
Title | cohomological complex of topological vector spaces |
Canonical name | CohomologicalComplexOfTopologicalVectorSpaces |
Date of creation | 2013-03-22 18:17:27 |
Last modified on | 2013-03-22 18:17:27 |
Owner | bci1 (20947) |
Last modified by | bci1 (20947) |
Numerical id | 22 |
Author | bci1 (20947) |
Entry type | Definition |
Classification | msc 55N99 |
Classification | msc 81T70 |
Classification | msc 32S20 |
Classification | msc 12G10 |
Classification | msc 55N33 |
Classification | msc 13D25 |
Classification | msc 18G35 |
Synonym | cohomological complex |
Related topic | HomologicalComplexOfTopologicalVectorSpaces |
Related topic | ChainComplex |
Related topic | CategoricalSequence |
Related topic | TangentialCauchyRiemannComplexOfCinftySmoothForms |
Related topic | ACRcomplex |
Defines | dual of chain complex |
Defines | cochain complex |
Defines | transpose map |
Defines | sequence of topological vector spaces |
Defines | sequence of continuous linear maps |