The paper introduces some preliminary notions concerning the Wroclaw taxonomy according to [14]. The classifications and tolerances are defined and considered w.r.t. sets and metric spaces. We prove theorems showing various classifications based on tolerances. In this paper A, X denote non empty sets, f denotes a partial function from [: X, X :] to R, and a denotes a real number. Let us observe...

In this paper A, X are non empty sets, f is a partial function from [:X, X :] to R, and a is a real number. Let us note that there exists a real number which is non negative. We now state a number of propositions: (1) For every finite sequence p and for every natural number k such that k + 1 ∈ dom p and k / ∈ dom p holds k = 0. (2) Let p be a finite sequence and i, j be natural numbers. Suppose...

1Department of Prosthetic Dentistry, Faculty of Medicine, Dresden University of Technology, 01307 Dresden, Germany 2Department of Prosthetic Dentistry, Faculty of Dentistry, Wroclaw Medical University, 50425 Wroclaw, Poland 3Department of Maxillofacial Orthopedics and Orthodontics, Faculty of Dentistry, Wroclaw Medical University, 50425 Wroclaw, Poland 4Department and Clinic of Rheumatology and...

Marek Cegielski1,4, Ilona Iżykowska1, Wojciech Dziewiszek2,4, Maciej Zatoński3, Marek Bochnia3,4 and Olga Kalisiak5 1Departments of Histology and Embryology, Medical University of Wroclaw 2 Departments of Pharmacology, Medical University of Wroclaw, 3Department of Otolaryngology, Faculty of Dentistry, Medical University of Wroclaw, 4Stem Cells spin Ltd. Wrocław Technology Park, Wroclaw, 5Depart...