We extend to topological affine planes the standard theorems of convexity, among them the separation theorem, the anti-exchange theorem, Radon’s, Helly’s, Carathéodory’s, and Kirchberger’s theorems, and the Minkowski theorem on extreme points. In a few cases the proofs are obtained by adapting proofs of the original results in the Euclidean plane; in others it is necessary to devise new proofs ...

1 Human Genome Center, Institute of Medical Science, The University of Tokyo, 4-6-1 Shirokane-dai, Minato-ku, Tokyo 108-8639, Japan; E-Mail: [email protected] 2 Graduate School of Information Sciences, Tohoku University, 6-3-09, Aramaki-aza-aoba, Aoba-ku, Miyagi, 982-0036, Japan; E-Mail: [email protected] 3 Bioinformatics Research and Development, Japan Science and Technology Corporation, 4-...

a) Department of Radiological Sciences, School of Health Sciences, Ibaraki Prefectural University of Health Sciences, Ami 4669-2, Ami-machi, Inashiki-gun, Ibaraki 300-0394, Japan b) MI clinic, Syouji 1-12-13, Toyonaka City, Osaka 560-0004, Japan c) National Institute of Public Health, Minami 2-3-6, Wako City, Saitama 351-0197, Japan d) Yokohama Rousai Hospital, Kodzukue-cho 3211, Kofuku-ku, Yok...

Department of Pharmaceutical Microbiology, Faculty of Life Sciences, Kumamoto University, 5-1 Oe-honmachi, Chuou-ku, Kumamoto 862-0973, Japan (S.O., K.N.) Laboratory of Veterinary Pathology, School of Veterinary Medicine, Azabu University, 1-17-71 Fuchinobe, Sagamihara, Kanagawa 229-8501, Japan (H.K., J.K.) Division of Membrane Transport and Drug Targeting, Graduate School of Pharmaceutical Sci...

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