  We study the dependence of Ly$\alpha$ escape from galaxies on UV continuum
size and luminosity using a sample of 40 Green Pea (GP) galaxies, which are the
best local analogs of high-redshift Ly$\alpha$-emitters (LAEs). We use the
Cosmic Origins Spectrograph near-ultraviolet images from the \textit{Hubble
Space Telescope} to measure the UV size and luminosity with $0.047''$ spatial
resolution. Like most galaxies the GPs show a log-normal size distribution.
They also show a positive correlation between size and UV-continuum luminosity.
The slope of the size-continuum luminosity relation for GPs is consistent with
those of continuum-selected star-forming galaxies at low and high redshifts. A
distinctive feature of GPs is a very compact typical radius of 0.33 kpc with a
population spread (1$\sigma$) of 0.19 kpc. The peak of the size distribution
and the intercept of the size-luminosity relation of GPs are noticeably smaller
than those of continuum-selected star-forming galaxies at similar redshifts.
There are statistically significant anti-correlations found between the
circularized half-light radius ($r_{\rm cir,50}$), the Ly$\alpha$ equivalent
width (EW(Ly$\alpha$)), and the Ly$\alpha$ escape faction
($f^{Ly\alpha}_{esc}$), suggesting that small UV-continuum radii are crucial
for Ly$\alpha$ emission. GPs and high-redshift LAEs have similar sizes, once
spatial resolution effects are properly considered. Our results show that a
compact/small size is crucial for escape of Ly$\alpha$ photons, and that
Ly$\alpha$-emitters show constant characteristic size independent of their
redshift.
