how are the openings in the Whitney $C^{k}(\mathbb{R}^{n},\mathbb{R}^{m})$ topology

Question

I am studying whitney topology in $\mathbb{R}^{n}$, the definition says:

1. let's consider $C^{\infty}(\mathbb{R}^{n},\mathbb{R}^{m})$.
2. Let $k\in \mathbb{Z}^{+}$, the we denote $M(U)=\lbrace f\in C^{\infty}(\mathbb{R}^{n},\mathbb{R}^{m}):j^{k}f(\mathbb{R}^{n})\subset U\rbrace$.

The set $\lbrace M(U):k\in \mathbb{Z}^{+}\rbrace$, where $U\subset J^{k}(\mathbb{R}^{n},\mathbb{R}^{m})$, forms a basis for a topology.

Where $j^{k}f(\mathbb{R}^{n})$, is the Taylor expansion to order k.

The definition confuses me a bit, I am not sure if the openings in this topology are jets, which are Taylor expansions, I have tried to give an example, I could not I have thought about considering functions that are equal at a point within the Taylor polynomial, but I am not sure