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In this paper we prove two mapping theorems on mesocompact spaces: (1) Perfect mappings preserve mesocompactness; (2) Closed mappings preserve normal mesocompactness. The main results of this paper are two mapping theorems on mesocompact spaces. Mesocompactness was defined in J. R. Boone  and studied by V. J. Mancuso  and J. R. Boone [4, 5]. Mancuso  intended to prove that perfect mappings preserve mesocompactness, but his proof was incorrect. J. R. Boone  noticed the error indoi:10.1090/s0002-9939-1983-0712651-5 fatcat:uxf2byqgdbe3xbu5ic7r2ngrga