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Abstract: The concept of continuity is familiar to us from our first calculus course, and in multivariable calculus, we learn how to extend this to R^2. In fact, the branch of mathematics known as topology generalizes continuity even more. In this talk we will explain the basics of this generalization, and study a particular example on R^2, called the "plus topology". Then, we will return to multivariable calculus and examine some of our old theorems with the help of the plus toplogy.
