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Point Open Set Metric Space Set Addition Superset Topological Space Sequence Limit Point

1	Point
1	Topological Space
1	Open Set
1	Metric Space
1	Sequence
1	Set
1	Superset
1	Addition
2	Limit Point

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Types Of Limit Points

Let be a topological space and $A\subset X$ be a subset.

A point $x\in X$ is an $\omega$ -accumulation point of if every open set in that contains also contains infinitely many points of .

A point $x\in X$ is a condensation point of if every open set in that contains also contains uncountably many points of .

If is in addition a metric space, then a cluster point of a sequence $\{x_n\}$ is a point $x\in X$ such that every $\epsilon>0$ , there are infinitely many point such that $d(x,x_n)<\epsilon$ .

These are all clearly examples of limit points.