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In this note we give several new characterizations of arbitrary pseudocompact spaces, that is spaces characterized by the property that all continuous real-valued functions on the space are bounded. Subject classification (Amer. Math. Soc. (MOS) 1970): primary 54 D 20, 54 C 30.doi:10.1017/s1446788700013410 fatcat:3uoial7mhjfqjbtpqev6ry4vqq