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A Künneth formula in topological homology and its applications to the simplicial cohomology of l<sup>1</sup>(Z<sub>+</sub><sup>k</sup>)
We establish a Künneth formula for some chain complexes in the categories of Fréchet and Banach spaces. We consider a complex ${\cal X}$ of Banach spaces and continuous boundary maps $d_n$ with closed ranges and prove that $H^n({\cal X}') \cong H_n({