Every chain functor ${f K}_{*}$ determines a homology theory on a given category of topological spaces resp. of spectra $H_{*}(f K_{*})(cdot)$ cf. S 4. If $f K_{*}$, ${f L}_{*}$ are chain functors such that $H_{*}({f K}_{*})(cdot) pprox H_{*}({f L}_{*})(cdot)$ then there exists a third chain functor ${f C}_{*}$ and transformations of chain functors ${}^{K}gamma :{f K}_{*} longrightarrow {f C}_{*}$, ${}^{L}gamma: {f L}_{*} longrightarrow {f C}_{*}$ inducing isomorphisms of the associated homology theories (theorem 1.1.). Moreover the distinction between regular and irregular chain functors is introduced.
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