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This paper recalls the work of D. Pompeiu who introduced the notion of set distance in his thesis published one century ago. The notion was further studied by F. Hausdor, C. Kuratowski who acknowledged in their books the contribution of Pompeiu and it is frequently called the Hausdor distance. keywords: Hausdor distance, Hausdor-P ompeiu distance, Pompeiu functions, Pompeiu conjecture, Schier conjecture 1 The thesis of Pompeiu

One Hundred Years Since the Introduction of the Set Distance by Dimitrie Pompeiu