  (Abridged) We present a study of the ionizing stars associated with the
diffuse ionized gas (DIG) and HII regions in the nearby spiral galaxy M33. We
compare our Schmidt H-alpha image to the far-ultraviolet (FUV, 1520A) image
from the Ultraviolet Imaging Telescope (UIT). The H-alpha/FUV ratio is higher
in HII regions than in the DIG, suggesting an older population of ionizing
stars in the DIG. When compared to models of evolving stellar populations, the
N(Lyc)/FUV ratio in HII regions is consistent with a young burst, while the DIG
ratio resembles an older burst population, or a steady state population built
up by constant star formation. The UIT data is complimented with archival FUV
and optical images of a small portion of the disk of M33 obtained with WFPC2 on
HST. Using the HST FUV and optical photometry, we assign spectral types to the
stars observed in DIG and HII regions. The photometry indicates that ionizing
stars are present in the DIG. We compare the predicted ionizing flux with the
amount required to produce the observed H-alpha emission, and find that field
OB stars in the HST images can account for 40% +/- 12% of the ionization of the
DIG, while the stars in HII regions can provide 107% +/- 26% of the H-alpha
luminosity of the HII regions. We do not find any correlation between leakage
of ionizing photons and H-alpha luminosity for the HII regions in these HST
fields. If stellar photons alone are responsible for ionizing the DIG, the
current results are consistent with no or few ionizing photons escaping from
the galaxy.
