FRagmentation and Evolution of dense cores Judged by ALMA (FREJA). I
  (Overview). Inner $\sim$1000 au structures of prestellar/protostellar cores
  in Taurus
  We have performed survey-type observations in 1 mm continuum and molecular
lines toward dense cores (32 prestellar + 7 protostellar) with an average
density of $\gtrsim$10$^5$ cm$^{-3}$ in the Taurus molecular clouds using the
Atacama Large Millimeter/submillimeter Array-Atacama Compact Array (ALMA-ACA)
stand-alone mode with an angular resolution of 6.$''$5 ($\sim$900 au). The
primary purpose of this study is to investigate the innermost part of dense
cores toward understanding the initial condition of star formation. In the
protostellar cores, contributions from protostellar disks dominate the observed
continuum flux with a range of 35-90% except for the very low-luminosity
object. For the prestellar cores, we have successfully confirmed continuum
emission from dense gas with a density of $\gtrsim$3 $\times$10$^5$ cm$^{-3}$
toward approximately one-third of the targets. Thanks to the lower spatial
frequency coverage with the ACA-7 m array, the detection rate is significantly
higher than that of the previous surveys, which have 0 or 1 continuum detected
sources among large number of starless samples using the ALMA Main array. The
statistical counting method tells us that the lifetime of the prestellar cores
until protostar formation therein approaches the free-fall time as the density
increases. Among the prestellar cores, at least two targets have possible
internal substructures, which are detected in continuum emission with the size
scale of $\sim$1000 au if we consider the molecular line (C$^{18}$O and
N$_2$D$^{+}$) distributions. These results suggest that small-scale
fragmentation/coalescence processes occur in a region smaller than 0.1 pc,
which may determine the final core mass associated with individual protostar
formation before starting the dynamical collapse of the core with central
density of $\sim$(0.3-1) $\times$ 10$^6$ cm$^{-3}$.
