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0-cells and 1-cells 1-cell joining 2-cells of Ct Analysis Situs boundary called cells of Cn Chap circuits closed curve closed manifold coefficients of torsion columns of Dk complete set complex Cn complex composed composed of cells defined definition deformation denoted determined elements equations Euclidean fc-cells fc-dimensional complex finite number follows fundamental group Hence homeomorphic homology i-cells incidence relations integers invariant factors J. W. Alexander l)-cells linear combination linear graph linear relation linearly dependent main diagonal Mobius band modulo n-dimensional negatively related non-singular normal form number of 0-cells obtained one-dimensional complex operations of type orientable manifold oriented 1-cells oriented complex oriented fc-circuits plex positively related proved regular subdivision rows and columns rth row set of 1-circuits set of oriented set of points simplex solutions sphere square matrix straight 1-cells sum mod theorem transformations triangle star two-dimensional complex two-dimensional manifold vertex vertices zero