Reconstruction of generalized cohomology theories by means of the notion of continuous functors

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We constructed a category of topological spaces which satisfies the properties suitable for developing homotopy theory, and used it to establish a method for defining generalized cohomology theories by means of the notion of bivariant functors. In comparison with the conventional construction given by spectra, our new construction is more systematic and is easier to extend to categories other than that of topological spaces ; hence we may expect it to be applied to a variety of problems.