Uniform continuity is a stronger form of continuity that ensures the function behaves consistently across its entire domain. Unlike regular continuity, which allows for different rates of change at different points, uniform continuity guarantees that for every small change in the output, there is a uniform limit on how much the input can change throughout the entire space. This property is especially significant when dealing with Lipschitz continuity and multifunctions, as it helps in establishing the stability of functions and their mappings.
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