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E25

[0PY] Prerequisites:[0P1],[0NH].

Let \(D(x,r){\stackrel{.}{=}}\{ y\in X : d(x,y)\le r\} \) be the disk, show that it is closed.

Let \(S(x,r){\stackrel{.}{=}}\{ y\in X : d(x,y)= r\} \) be the sphere, show that it is closed.

Solution 1

[0PZ]

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