trivial topology example

Let X be a set. Let X be a set. In general, the discrete topology on X is T = P(X) (the power set of X). The points are so connected they are treated like a single entity. Examples: If is a metric on and if and only if for all , there exists such that . Why is topology even an issue? In the case that the space of field configurations has non-trivial topology, the role of non -trivial homotopy of paths of field configurations is discussed. In order to do that, we need to ﬁnd, for each >0, a value >0 such that jf(x) Lj< whenever x2Uand 0
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