The atmospheric Cerenkov imaging technique has been used to search for point-like and diffuse TeV gamma-ray emission from the southern supernova remnant, W28, and surrounding region. The search, made with the CANGAROO 3.8m telescope, encompasses a number of interesting features, the supernova remnant itself, the EGRET source 3EG J1800-2338, the pulsar PSR J1801-23, strong 1720 MHz OH masers and molecular clouds on the north and east boundaries of the remnant. An analysis tailored to extended and off-axis point sources was used, and no evidence for TeV gamma-ray emission from any of the features described above was found in data taken over the 1994 and 1995 seasons. Our upper limit (E>1.5 TeV) for a diffuse source of radius 0.25deg encompassing both molecular clouds was calculated at 6.64e-12 photons cm^-2 s^-1 (from 1994 data), and interpreted within the framework of a model predicting TeV gamma-rays from shocked-accelerated hadrons. Our upper limit suggests the need for some cutoff in the parent spectrum of accelerated hadrons and/or slightly steeper parent spectra than that used here (-2.1). As to the nature of 3EG J1800-2338, it possibly does not result entirely from pi-zero decay, a conclusion also consistent with its location in relation to W28.
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