limit point (original) (raw)
Equivalently:
- •
x is a limit point of A if and only if there is a net in A converging to x which is not residually constant. - •
x is a limit point of A if and only if there is a filter on A converging (http://planetmath.org/filter) to x. - •
If X is a metric (or first countable) space, x is a limit point of A if and only if there is a sequence of points in A∖{x} converging to x.
| Title | limit point |
|---|---|
| Canonical name | LimitPoint |
| Date of creation | 2013-03-22 12:06:51 |
| Last modified on | 2013-03-22 12:06:51 |
| Owner | mathcam (2727) |
| Last modified by | mathcam (2727) |
| Numerical id | 15 |
| Author | mathcam (2727) |
| Entry type | Definition |
| Classification | msc 54A99 |
| Synonym | accumulation point |
| Synonym | cluster point |
| Related topic | AlternateStatementOfBolzanoWeierstrassTheorem |