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The spaces $\Omega_n(m)$ that generalize the spaces $\Omega_n$ are introduced. In order to investigate the homotopy invariants of the space $\Omega_n(m)$ the CW-structure of the space $\Omega_n(m)$ is built. Using exact homology sequence the homology groups of the space $\Omega_n(m)$ are calculated.doi:10.15421/241904 fatcat:pr2qilskj5eqboprzbzz42q5s4