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

A point $x\in X$ is an <</SPAN>#99#>$\omega$ accumulation point of $A$ if every open set in $X$ that contains $x$ also contains infinitely many points of $A$

A point $x\in X$ is a <</SPAN>#100#>condensation point of $A$ if every open set in $X$ that contains $x$ also contains uncountably many points of $A$

If $X$ 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 $x_n$ such that $d(x,x_n)<\epsilon$

These are all clearly examples of limit points.