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Let G be a topological group and let G-E-E-*BG be the universal fibration for G so that B G iS the classifying space for G. Eilenberg and Moore have developed two spectral sequences which deal with this situation [1], [2], [3]. The spectral sequence of Type I has E2 = CotorH*(G)(K, K)=>H* [BG]. The Type II spectral sequence has E2= TorH*[BG] (K, K)=>H* [G]. K is the ground ring. These tools give a very simple proof of

The Eilenberg-Moore, Rothenberg-Steenrod spectral sequence for 𝐾 theory