What would be the space of section of the bundle $\mathfrak{g}\longrightarrow \{e\}$?

Question

Let $\mathfrak{g}$ be a Lie algebra and $\pi:\mathfrak{g}\longrightarrow \{e\}$a vector bundle over a point. What would be the sections of this bundle?

Answer 1

Well, the sections are maps from a point onto its fiber; the only maps from a point to its fiber are the constant maps $f(e)=g$ ; for g in $\mathfrak{g}$. But the bundle is trivial, since a single point is contractible ( or maybe "contracted" already), which makes sense, in that $\mathfrak{g}=\mathfrak{g} \times ${$e$} .