The present application pertains to the field of cosmetics, more specifically the field of topical care of bad odors, by the action of a bactericidal and/or bacteriostatic topical composition, and of capturing odors. The topical composition according to the invention comprises at least one cyclodextrin, a 1,4-3, 6-dianhydrohexitol and/or a 1,4-3, 6-dianhydrohexitol derivative. It can be useful for the oral sphere, but also for areas of the skin where bad odors may develop due to microbial activity, namely the underarms, crotch and feet. Preferably, the topical composition of the invention is used for treating the oral sphere, most preferably for treating halitosis.