Having defined the simplicial homology groups of a polyhedron (space of a general simplicial complex) now we come to another kind of homology groups, called singular homology groups of a topological space. The first interesting feature of these homology groups is that they are defined for all topological spaces X, not only for polyhedra. Singular homology groups were first defined by S. Lefschetz in 1933, and were perfected in their present form by S. Eilenberg (1913–1998) in the beginning of the 1940’s.
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