Isolated Point - Examples

Examples

Topological spaces in the following examples are considered as subspaces of the real line.

  • For the set, the point 0 is an isolated point.
  • For the set, each of the points 1/k is an isolated point, but 0 is not an isolated point because there are other points in S as close to 0 as desired.
  • The set of natural numbers is a discrete set.
  • The Morse lemma states that non-degenerate critical points of certain functions are isolated.

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