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We prove some results on the farthest points in convex metric spaces and in linear metric spaces. The continuity of the farthest point map and characterization of strictly convex linear metric spaces in terms of farthest points are also discussed. 2010 Mathematics Subject Classification: 46B20, 46B99, 46C15, 46C99, 41A65. Key words and phrases: Chebyshev centre, convex metric space, externally convex metric space, farthest point, farthest point map, M -space, strictly convex linear metricdoi:10.2298/pim1409229s fatcat:aglbdyxq7ba3lerk5fsh5ilna4