Definition 0.1. A homological complex of topological vector spaces is a pair (E∙,d), where
E∙ = (Eq)q∈Z is a sequence of topological vector spaces and d = (dq)q∈Z is a sequence of
continuous linear maps dq from Eq+1 into Eq which satisfy dq ∘ dq+1 = 0.
0.1 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.
