Isolated Point

Examples

• For the set $S=\backslash \{0\backslash \}\backslash cup2$, the point 0 is an isolated point.

• For the set $S=\backslash \{0\backslash \}\backslash cup\; \backslash \{1,\; 1/2,\; 1/3,\; \backslash dots\; \backslash \}$, 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 N={0, 1, 2, ...} of natural numbers is a discrete set.

See also

• discrete space

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