So I just recently started to study foliation theory and I realized I'm visualizing plaques of foliations the wrong way.
Given a manifold $M$, a foliation $\mathcal{F}$ of the manifold and a local chart $(U,\varphi)$ of $\mathcal{F}$ such that $\varphi(U)=U_1 \times U_2 \subset \mathbb{R}^n \times \mathbb{R}^{m-n}$, my definition of a plaque ($\alpha$) is a set of the form $\varphi^{-1}(U_1 \times \{c\}), \enspace c \in U_2$.
In my head, I imagine a plaque simply being the intersection of a leaf $F$ of the foliation and my open set $U$ of $M$.
For some time this made sense to me until I came across the observation that, in the topology of the leaf $F$, one could have $F$ intercepting the domain $U$ of a chart $(U,\varphi)\in \mathcal{F}$ in a sequence of plaques $(\alpha_n)_{n\in\mathbb{N}}$, which accumulate in a plaque $\alpha \subset F$.
For me, this is not coherent with the image I had of a plaque because, given a domain $U$ and a leaf $F$, I could only have one plaque of $F$ in $U$.
What is the problem here? I would appreciate any help. Please be kind since I have just recently started to study this.
With a tiny change, you can convert your incorrect intuition into a correct intuition, like this: A plaque is a connected component of the intersection of a leaf $F$ and the open set U.