Representation of the maximal ideal space as a fiber product

This paper investigates the relationship between the topological structure of the maximal ideal space of a commutative C*-algebra and the topological structures of the maximal ideal spaces of its subalgebras. A theorem is proved regarding the embedding of the spectrum of the algebra under consideration into the fiber product of the spectra of its subalgebras. A criterion for the coincidence of the spectrum with the specified fiber product is formulated. As an application, the method described above is used to describe the topology of the spectra of algebras of discontinuous functions.

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