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A Metric Space is a set with a concept of distance. That concept is embodied in a function which is called a *metric.* More formally, given a set, a metric on that set is a function /d(x,y)/ that takes two elements and returns a real number. The metric has to satisfy the following conditions: * EQN:d(x,x)=0 * EQN:d(x,y)=d(y,x) * EQN:d(x,y)+d(y,z){\ge}d(x,z) Exercise: Using the above, prove that EQN:d(x,y){\ge}0. From Metric Spaces we can get the concept of Open Sets, which in turn leads to the idea of a topological space, which manages to keep the concept of closeness, without requiring the concept of distance.