Difference between revisions of "Limit point"
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Latest revision as of 16:50, 28 March 2009
When is a metric space, it follows that every neighborhood of must contain infinitely many elements of . A point such that each neighborhood of contains uncountably many elements of is called a condensation point of .
- Let be the space of real numbers (with the usual topology) and let , that is the set of reciprocals of the positive integers. Then is the unique limit point of .
- Let and be the set of rational numbers. Then every point of is a limit point of . Equivalently, we may say that is dense in .
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