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We investigate the evolution of compact galaxy number density over the redshift range $0.2<z<0.8$. Our sample consists of galaxies with secure spectroscopic redshifts observed in the COSMOS field. With the large uncertainties, the compact galaxy number density trend with redshift is consistent with a constant value over the interval $0.2<z<0.8$. Our number density estimates are similar to the estimates at $z>1$ for equivalently selected compact samples. Small variations in the abundance of the COSMOS compact sources as a function of redshift correspond to known structures in the field. The constancy of the compact galaxy number density is robust and insensitive to the compactness threshold or the stellar mass range (for $M_\ast>10^{10}\, M_\odot$). To maintain constant number density any size growth of high-redshift compact systems with decreasing redshift must be balanced by formation of quiescent compact systems at $z<1$.

QUIESCENT COMPACT GALAXIES AT INTERMEDIATE REDSHIFT IN THE COSMOS FIELD. THE NUMBER DENSITY