The abstract, multidimensional varieties and their classification - Mariana Bujac; Petru Soltan (Journal of Numerical Analysis and Approximation Theory, 2004)
We define abstract multidimensional variety without borders, using the investigation of the complex of multi-ary relations (H. Martini and P. Soltan, 2003 [3]) and the notion of compact, combinatorial, multidimensional variety without borders (V. G. Boltyanski and V. A. Efrimovici, 1982 [1]). We indicate the classification of this kind of varieties similarly to the results of classification of compact, two-dimensional surfaces without borders (V. G. Boltyanski and V. A. Efrimovici, 1982 [1]). We use varieties' genders (modulo Euler characteristic (V. G. Boltyanski, 1995 [2])) to classify them.