A set $A$ is said to be almost clopen if it can be uniquely represented in the form $A=B\Delta M$, where $B$ is a clopen set, $M$ is a set of first category (or meagre), and $\Delta$ denotes the operation of symmetric difference. In other words, we have $A\Delta B=M$, which, in some sense, means that the difference between an almost clopen set and a clopen set is small/negligible.
But what does that mean in practice? In particular, if a clopen set $B$ has a property P, does the corresponding almost clopen set $A$ have property $P$ (perhaps adding something like "off a first category set")?
For example, if a set $B$ is clopen, then ${\rm Int}\ B={\rm Cl}\ B$ (the interior of $B$ = the closure of $B$). Does this property hold for an almost clopen set $A$, i.e., do we have ${\rm Int}\ (B\Delta M)={\rm Cl}\ (B\Delta M)$ or equivalently ${\rm Int}\ A={\rm Cl}\ A$ (perhaps adding "off a first category set")?