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:
“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)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)