Borodin's Theory of Gaps

Borodin's Theory of Gaps suggests that gaps or discontinuities naturally occur in the structure of mathematical objects, such as sets or functions, when they are constructed or analyzed in steps. These gaps reflect regions where certain properties or elements are missing, revealing the limits or boundaries within the mathematical system. The theory highlights that such discontinuities are not accidental but integral to understanding complex structures, emphasizing the importance of examining these "gaps" to gain deeper insights into the behavior and organization of mathematical entities.