  We have obtained Hubble Space Telescope WFPC2 2200 A and optical V-band
images of 20 low-luminosity active galactic nuclei, most of which are
spectroscopically classified as LINERs, in order to search for a possible
photoionizing continuum. Six (30%) of the galaxies are detected in the UV. Two
of the detected galaxies (NGC 3642 and NGC 4203) have compact, unresolved
nuclear UV sources, while the remaining four UV sources (in NGC 4569, NGC 5005,
NGC 6500, and NGC 7743) are spatially extended. Combining our sample with that
of Maoz et al. (1995), we find that the probability of detection of a nuclear
UV source is greatest for galaxies having low internal reddening and low
inclination, and we conclude that dust obscuration is the dominant factor
determining whether or not a UV source is detected. Large emission-line
equivalent widths and the presence of broad-line emission also increase the
likelihood of detection of nuclear UV emission. Our results suggest that the
majority of LINERs harbor obscured nuclear UV sources, which may be either
accretion-powered active nuclei or young star clusters. Under the assumption
that the compact UV sources in NGC 3642 and NGC 4203 have nonstellar power-law
spectra extending into the extreme ultraviolet, the extrapolated ionizing
fluxes are sufficiently strong to photoionize the narrow-line regions of these
objects. The V-band images of many galaxies in our sample reveal remarkably
strong dust lanes which may be responsible for obscuring some UV sources.
