EDB — 0Q7

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E47

[0Q7] Prerequisites:Section  [2BK].Let \((M,d)\) be a metric space and suppose that there exists \(D⊆ M\) that is countable and dense. Such \((M,d)\) is called separable. Show that \((M,d)\) satisfies the second axiom of countability.

The converse is true in any topological space, see [0MH].

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Authors: "Mennucci , Andrea C. G." .
Bibliography
Book index
  • separable space
  • second axiom of countability
  • axiom, second --- of countability
  • accumulation point, in metric spaces
  • topology, in metric spaces
  • metric space
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