How to translate relative closure into convergence of sequences? There is a usual property/definition of closed set: for any convergent sequence of elements in the set, its limit belongs to the closed set itself.
Let's have $Y\subset X$, where $Y$ is a subspace of $X$.
The relative closure of $A$ with respect to $Y$ is
$$\text{cl}_Y(A)=\text{cl}_X(A)\cap Y.$$
How do we translate this into a property of convergent sequences?

$A$ is relatively closed (= closed in the subspace topology) iff for every net (sequences don't suffice in general, but only for first-countable spaces) in $A$ which is convergent in $X$ to a limit in $Y$ this limit is actually in $A$.
