What does "minus the zero section" mean?

Question

I see a vector bundle obtained from another one by the means of "minus the zero section" in some literature. The concept zero section of a vector bundle is found in Section Sections and locally free sheaves here. But as one can see, this zero section is not something in the vector bundle, but a continuous map. How can I "minus" or subtract a zero section from a vector bundle? Is there an example? Thanks.

Answer 1

"Minus the zero section" means you remove the zero section from the total space. For example, the trivial bundle $X \times \mathbb{R}^n$ over $X$, minus the zero section, is $X \times (\mathbb{R}^n \setminus \{ 0 \})$.