Example of $\pi$-metrizable space 
A tychonoff space $X$ is $\pi$-metrizable if and only if it has a $\sigma$-locally finite
  $\pi$-base.

Please help me to find some example of $\pi$-metrizable space. 
Is it true that every $\pi$-metrizable space is a moscow space ?

For a space $X$,
A collection of nonempty open sets $\mathcal{A}$ , is called a $\pi$-base if for every nonempty
open set $O$, there exists $U \in\mathcal{A}$  such that $U\subset O$.
 A: Theorem $3.4$ of Derrick Stover, ‘On $\pi$-metrizable spaces, their continuous images and products’, says that if $X$ is any Tikhonov space, and $D$ is the discrete space of cardinality $\pi w(X)$, then $X\times D^\omega$ is $\pi$-metrizable; that provides quite a few examples. In particular, let $\kappa$ be any infinite cardinal, let $D$ be the discrete space of cardinality $\kappa$, and let $X=D^\kappa$. Then $d(X)=\kappa$ by the Hewitt-Marczewski-Pondiczery theorem, so $\pi w(X)=\kappa$, and $X\cong X\times D^\omega$ is $\pi$-metrizable.
However, it follows from Corollary $2.12$ of A. V. Arhangel’skiǐ, Moscow spaces and topological groups, Top. Proc. 25 (2000), 383-416, that if $X\times D^\omega$ is Moscow, then so is $X$. Thus, $X\times D^\omega$ is a $\pi$-metrizable space that is not Moscow if $X$ is not Moscow.
A: Some other examples:

Example 1: Every discrete space $X$ has a $\sigma$-locally finite $\pi$-base.
Example 2: $\mathbb R$ with the uaual topology has a $\sigma$-locally finite $\pi$-base.

