EDB — 0GY

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Definition 18

[0GY] Given \(A⊆ X\), a point \(x∈ X\) is an accumulation point for \(A\) if, for every neighborhood \(U\) of \(x\), \(U∩ A⧵\{ x\} \) is not empty.  1

The set of all accumulation points of \(A\) is called derived set and will be indicated with \(D(A)\).

  1. We could call \(U⧵\{ x\} \) a ”deleted neighborhood”; so we are asking that the deleted neighborhood \(U⧵\{ x\} \) has non-empty intersection with \(A\); as we already did in [0BG].
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Authors: "Mennucci , Andrea C. G." .
Bibliography
Book index
  • accumulation point, in a topological space
  • deleted neighborhood, in a topological space
  • neighborhood, deleted, in a topological space
  • set, derived ---
  • space, topological
  • topological space
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