Limit points

Limit points of a set should also not be confused with boundary points. For example, ${\displaystyle 0}$ is a boundary point (but not a limit point) of the set ${\displaystyle \{0\}}$ in ${\displaystyle \mathbb {R} }$ with standard topology. However, ${\displaystyle 0.5}$ is a limit point (though not a boundary point) of interval ${\displaystyle [0,1]}$ in ${\displaystyle \mathbb {R} }$ with standard topology (for a less trivial example of a limit point, see the first caption).