limit point
Noun
Meaning
the mathematical value toward which a function goes as the independent variable approaches infinity
Source: WordNetSynonyms
Hypernyms
Examples
A compact uniform space is complete: on a compact space each filter has a cluster point, and if the filter is Cauchy, such a cluster point is a limit point.
It is also a limit point of the set of limit points.
Moreover, every cluster point of a Cauchy filter is a limit point.
Roughly speaking, a function is right-continuous if no jump occurs when the limit point is approached from the right.
The process could then be repeated by dividing the resulting smaller interval into smaller and smaller parts until it closes down on the desired limit point.
Therefore, (x n ) is a Cauchy sequence in E, converging to some limit point a in E, because E is complete.