  In this paper we present the results of a high resolution (5") CARMA and SZA
survey of the 3mm continuum emission from 11 of the brightest (at 1.1mm)
starless cores in the Perseus molecular cloud. We detect 2 of the 11 cores,
both of which are composed of single structures, and the median 3 sigma upper
limit for the non-detections is 0.2 M_sun in a 5" beam. These results are
consisent with, and as stringent as, the low detection rate of compact 3mm
continuum emission in dense cores in Perseus reported by Olmi et al. (2005).
From the non-detection of multiple components in any of the eleven cores we
conclude that starless core mass functions derived from bolometer maps at
resolutions from 10"-30" (e.g. with MAMBO, SCUBA or Bolocam) are unlikely to be
significantly biased by the blending of lower mass cores with small
separations. These observations provide additional evidence that the majority
of starless cores in Perseus have inner density profiles shallower than r^-2.
