👉 Uniform mathematics, also known as uniform analysis or uniform convergence, is a branch of mathematics that studies the behavior of sequences and series of functions over uniformly bounded domains. It focuses on properties that hold true for all points in a domain simultaneously, rather than just pointwise. Key concepts include uniform convergence of sequences of functions, where the rate at which functions approach a limit function is controlled uniformly across the domain, and uniform continuity, where functions behave well in terms of closeness over the entire domain. This approach is crucial in functional analysis, partial differential equations, and other areas of mathematics where understanding global behavior is essential.
