What is the topology on the product bundle

Question

If $X$ is a topological Space and $V$ is a vector Space then $X\times V$ forms a vector bundle over $X$, but I do not understand how do we topologise the space $X\times V$ so that it forms a vector bundle over $X$.

Answer 1

$V$ already has a topology usually (e.g. it's isomorphic to $\mathbb{R}^n$ or $\mathbb{C}^n$) and then we just use the product topology on $X \times V$, which makes both projections continuous (the one onto $X$ is what makes it a vector bundle)