What does it mean when one says "$B$ has no limit point in $A$"? If $B$ is a subset of a set $A$, what does the sentence "$B$ has no limit points in $A$" mean? I am aware that $x$ is a limit point of $A$, if for every neighbourhood $U$ of $x$, $(U-\{x\})\cap A$ is non-empty.
Please let me know. Thank you.

Giving an example may be helpful for you. 

Example: Let $X=\mathbb R$ with usual topology. $A=\{x\in \mathbb R: x > 0\} \subseteq X$ and $B=\{1, \frac12, \frac13,... \frac1n,...\} \subset A$. It is not difficult to see that $B$ has no limit points in $A$ since the unique limit point 0 of $B$ is not in $A$.

