Difference between revisions of "Limit point"
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<math>x</math> is a limit point of <math>A</math> if <math>x\in\text{Closure}(A-\{x\})</math> (you can read about [[Closure|closure here]]) | <math>x</math> is a limit point of <math>A</math> if <math>x\in\text{Closure}(A-\{x\})</math> (you can read about [[Closure|closure here]]) | ||
{{Todo|Prove these are the same}} | {{Todo|Prove these are the same}} | ||
| + | ==Other names== | ||
| + | * Accumilation point | ||
==Examples== | ==Examples== | ||
===<math>0</math> is a limit point of <math>(0,1)</math>=== | ===<math>0</math> is a limit point of <math>(0,1)</math>=== | ||
Revision as of 00:35, 13 February 2015
Contents
[hide]Definition
Common form
For a Topological space (X,J), x∈X is a limit point of A if every neighborhood of x has a non-empty intersection with A that contains some point other than x itself.
Equivalent form
x is a limit point of A if x∈Closure(A−{x}) (you can read about closure here)
TODO: Prove these are the same
Other names
- Accumilation point
Examples
0 is a limit point of (0,1)
Proof using first definition
Is is clear we are talking about the Euclidian metric
