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Uniform Topology

  • Definition: Given an index set J, and given points x = (x_a), a in J, and y = (y_a), a in J, of R^J, let us define a metric P(x,y) = sup{D(x_a, y_a)|a in J}, where D is the standard bounded metric on R. It is easy to check that P is indeed a metric; it is called the uniform metric on R^J, and the topology it induces is called the uniform topology.

    Source: Topology (second edition) by James R. Munkres

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