PlanetPhysics/Homological Complex of Topological Vector Spaces

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 [[../CoIntersections/|topological]] [[../NormInducedByInnerProduct/|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 [[../TrivialGroupoid/|homomorphisms]] is said to be a $R$-complex.