  Structural phase separation in A$_x$Fe$_{2-y}$Se$_2$ system has been studied
by different experimental techniques, however, it should be important to know
how the electronic uniformity is influenced, on which length scale the
electronic phases coexist, and what is their spatial distribution. Here, we
have used novel scanning photoelectron microscopy (SPEM) to study the
electronic phase separation in K$_x$Fe$_{2-y}$Se$_2$, providing a direct
measurement of the topological spatial distribution of the different electronic
phases. The SPEM results reveal a peculiar interconnected conducting
filamentary phase that is embedded in the insulating texture. The filamentary
structure with a particular topological geometry could be important for the
high T$_c$ superconductivity in the presence of a phase with a large magnetic
moment in A$_x$Fe$_{2-y}$Se$_2$ materials.
