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The HST/GHRS + G160M grating was used to obtain high resolution spectra of four very bright AGN located behind voids in the nearby distribution of bright galaxies (i.e. CfA and Arecibo redshift survey regions). A total of 9 Ly$\alpha$ absorption lines were discovered ranging in equivalent widths from 28 to 240 m\AA\ at velocities of $cz=1500-10000$~km/s. Of these 9, we identify 7 with supercluster structures and two in voids: one in the sightline of Mrk~501 at $cz=7740$~km/s and one in the sightline of Mrk~421 at $cz=3020$~km/s. Optical spectroscopy at Palomar and redshifted HI imaging at Westerbork fail to find faint galaxies or HI clouds close to the void absorption system in the Mrk 501 case. Thus, the voids are not entirely devoid of matter and not all Ly$\alpha$ clouds are associated with galaxies. Also, since the pathlengths through voids and superclusters probed by our observations thus far are nearly equal, there is some evidence that statistically the Ly$\alpha$ clouds avoid the voids. The nearest galaxy neighbors to these absorbing clouds are 0.45--5.9 Mpc away and thus too far away to be physically associated by most models, although some of the smaller nearest neighbor distances suggest a tidal debris origin to these clouds. Our results on local Ly$\alpha$ clouds are in full agreement with those found by Weymann, Morris et al. for the 3C273 sightline but disagree with results for the higher equivalent width systems where much closer cloud-galaxy associations were found by Lanzetta et al.
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