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 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.