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Set theory is a fundamental branch of mathematical logic that studies sets, which are collections of objects. In the context of fractal geometry, set theory provides the foundation for understanding and describing complex geometric structures. It enables the precise definition of concepts such as open and closed sets, limit points, and compactness, which are essential in the study of fractals. Set theory also facilitates the analysis of the properties and behavior of these sets, contributing to a deeper understanding of fractal geometry within the broader contexts of science and mathematics.