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.

Read more about this topic:  Isolated Point

Famous quotes containing the word examples:

    “No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
    —André Breton (1896–1966)

    “In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
    —Michel de Montaigne (1533–1592)

    “Histories are more full of examples of the fidelity of dogs than of friends.”
    —Alexander Pope (1688–1744)