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E21

[0PR] Let EβŠ†X, then E is a metric space with the restricted distance d~=d|EΓ—E.

Show that AβŠ†E is open in (E,d~) (as defined at the beginning of this section) if and only there exists a set VβŠ†X open in (X,d) such that V∩E=A.

(The second way of defining ”open” is used in topology.)

Solution 1

[2GD]

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Bibliography
Book index
  • accumulation point, in metric spaces
  • topology, in metric spaces
  • metric space
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