Let $S$ be a K3 surface and $\pi:S\rightarrow B$ be a SLAG $T^2$-fibration. I am struggling with a statement that

Fiberwise dualization does not change the topology of $S$.

Here by fiberwise dualization I mean dualizing smooth fibers and compactifying the dual fibration (I think this is the standard definition).

- My first question is, what do people mean by "compactification"?

Here is what I naively thought. Let $X$ be a Calabi--Yau n-fold and $\pi:X\rightarrow B$ a SLAG $T^n$-fibration. Let $B_0 \subset B$ be the set on which $\pi$ is smooth. Then $\pi^{-1}(B_0)$ and its dual $\pi^{-1}(B_0)^\vee$ is topologically the same, so we may compactify $\pi^{-1}(B_0)^\vee$ to get the original $X$. This should not happen in the SYZ picture. Of course this only holds at the topological level and ignores complex structure etc.

- My second question is, what makes difference between dimension two and higher?

The statement above is certainly not true in dimension three or higher. Otherwise SYZ mirror conjecture does not produce a mirror Calabi--Yau manifold, which in general has different topological type from the original one.