Domain Theory is a mathematical framework used in computer science to model the semantics of programming languages. It provides a way to describe the behavior of computations by using partially ordered sets, known as domains, which represent different states of a computation. Each element in a domain corresponds to a possible value or state, allowing for a structured way to analyze how programs execute and how they can converge to results. In Domain Theory, the concept of continuity is essential, as it helps to understand how functions behave over these domains. A function is continuous if it preserves the limits of directed sets, meaning that small changes in input lead to small changes in output. This property is crucial for reasoning about denotational semantics, which assigns mathematical meanings to programming constructs, facilitating the understanding of program behavior and correctness.