How to define a b-open set relative to a larger set?

Question

In the paper of D. Andrijevic entitled "On b-open Sets", it is defined that

A subset $S$ of a topological space $(X,\tau)$ is $b$-open if

$$ S\subseteq\bar{\operatorname{int} S}\cup \operatorname{int}\bar{S}$$

Now, if $A\subseteq B\subseteq X$, how to define the concept of "$A$ is $b$-open relative to $B$"?

Answer 1

$S$ is b-open if it is in the topology on $Y$ and $S\subset\overline{\mathrm{int}(S)}\cup \mathrm{int}(\overline{S})$

Where in general $\rm int$, is the interior of a set which is the union of all open sets contained in the set.