Definition 0.1 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.
