reproducing kernel hilbert space notation

Question

I'm trying to understand reproducing kernel Hilbert spaces (RKHSs) from scientific papers, however I don't find any gentle introduction. However, my main problem, at the moment, seems to be to understand the used notation. I understand that a kernel $k$ is a function which maps features to the respective inner product in a Hilbert space, i.e. $k(x,z)=<\phi(x), \phi(z)>_H$ with $\phi$ mapping from the original space to an Hilbert space. However, what I don't understand is the $(\cdot)$ notation, e.g. $k(\cdot, z)$. What means the dot instead of the first argument? In several papers I read something like $k(\cdot, z)=\phi(z)$ but what is the meaning of this? Intuitively I would think something like this: $\forall x, k(x, z)=\phi(z)$, but it does not seem to make any sense to me... Also the following answer Reproducing Kernel Hilbert Space - notation and basics does not clarify my doubts... So, what is the real meaning of $\cdot$? Does anyone know any clear introduction on this topic?