What are the types of continuity?

Continuity is a fundamental concept in mathematics that states the smooth transition of functions across their domain. There are different types of continuity that can be defined based on the characteristics of the function. The most basic is pointwise continuity, which means that the function is continuous at each point of its domain. Uniform continuity goes a step further by requiring a more consistent behavior of the function across its entire domain. Another type is Lipschitz continuity, which places a restriction on the rate of change of the function. And finally, there is the concept of absolute continuity, which deals with the relationship between the function and its derivative. Each type of continuity has its own set of criteria and applications in both pure and applied mathematics.

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