ABSTRACT
General topology has to do with, among other things, notions of convergence. Given a sequence xn of points in a set X, convergence of xn to a point χ can be defined in different ways. One of the main ways is by a metric, or distance d, which is nonnegative and real-valued, with xn → χ meaning d(xn, x) → 0. The usual metric for real numbers is d(x, y) = |x – y|. For the usual convergence of real numbers, a function f is called continuous if whenever xn → χ in its domain, we havef(xn ) → f(x).
