cohomological complex of topological vector spaces


Definition 0.1.

A cohomological complex of topological vector spaces is a pair (E,d) where (E=(Eq)qZ is a sequence of topological vector spaces and d=(dq)qZ is a sequence of continuous linear maps dq from Eq into Eq+1 which satisfy dqdq+1=0.

Remarks

  • The dual complex of a cohomological complex (E,d) of topological vector spacesMathworldPlanetmath is the homological complex (E,d) (http://planetmath.org/HomologicalComplexOfTopologicalVectorSpaces), where (E=(Eq)qZ with Eq being the strong dual of Eq and d=(dq)qZ , and also with dq being the transpose map of dq.

  • A cohomological complex of topological vector spaces (TVS) is a specific case of a cochain complexMathworldPlanetmathPlanetmath, which is the dual of the concept of chain complexMathworldPlanetmath.

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