EDB — 0QF

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E50

[0QF] Difficulty:**.Find an example of a metric space where for every \(x∈ X,r{\gt}0\), \(B_ r(x)\) is a closed set, but the associated topology is not discrete.  1

Solution 1

[0QG]

We note that such a space must be totally disconnected as shown in [0K0].

[ [0QH]]

  1. See [2F6] for the definition.
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Authors: "Mennucci , Andrea C. G." .
Bibliography
Book index
  • discrete topology
  • topology, discrete
  • space, totally disconnected ---
  • accumulation point, in metric spaces
  • topology, in metric spaces
  • metric space
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