Journal of Numerical Analysis and Approximation Theory (Aug 2004)
The abstract, multidimensional varieties and their classification
Abstract
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.