My question is really simple, what is the dimension of $A-B$, where $B$ is a subspace of $A$? this space is well-defined? I found this space in this paper on page 440:
Following my calculations in the paper, we would have $\dim(A-B)=\dim(A)-\dim(B)$, is that right? if not, maybe the author made a confusion and he should have written $\dim(\Omega^3(2D)/W)$ instead of $\dim(\Omega^3(2D)\setminus W)$?
Thanks in advance
If $B$ is a subspace of $A$, then $A-B$ is not in general a vector space, so $\dim(A-B)$ is not well-defined. For example, $$B=\mathbb{R}\times\{0\}=\{(x,0):x\in\mathbb{R}\}$$ is a subspace of $A=\mathbb{R}^2$, but $$A-B=\{(x,y)\in\mathbb{R}^2:y\neq 0\}$$ is not a vector space.
In fact, it is never a vector space because $0\notin A-B$.