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This paper investigates the atom set of a finite sigma-algebra and the reduct of a generator based on rough set theory.We show that the atom set of a given sigma-algebra is determined by its generator.In addition,the condition under which two generators produce the same sigma-algebra based on rough set theory is proposed.The condition of neighborhoods to form a partition is then investigated.Finally,the concept of reducts of a generator is introduced.We show that the method of attribute reduction in information systems can be used to obtain all the reducts of a generator.