Abstract
Possibilities to expand the experience of mathematics in studying abstract spaces for economics are considered. The concept of an abstract economic space is proposed, making it possible to bring to a new operational level the classification of economic spaces developed by F. Perroux in the late 1940s. Methodologically universal methods of ordering cognitive mappings of space are discussed, and the opportunities to use them within this concept are assessed. Based on one of the methods presented and employing the system of different geometries, essential variations in the subject of research of the spatial organization of economic activity are analyzed. The three types of economic space identified by Perroux are characterized in the context of the formalizations used for them: the affine group is assigned to space as defined by a plan; the group of conditional projective transformations, to space as a field of forces; and the group of topological transformations, to space as a homogeneous aggregate. The conclusion is reached that of principal importance in a space of the first type is the form of the boundaries between elements; in a space of the second type, the cooperative productivity of elements; and in a space of the third type, the quality of connections between elements.
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Notes
One can judge about the results by turning not only to the famous works by W. Isard [21, 22], W. Bunge [23], and P. Haggett [24] but also, for example, to Encyclopedia of Distances, published in honor of M. Fréchet and F. Hausdorff, who proposed and developed the concept of abstract spaces as sets of elements of an arbitrary nature [25].
For more detail on the opportunities to develop tools of studying multidimensional economic spaces, see [33].
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Translated by B. Alekseev
RAS Academician Pavel Aleksandrovich Minakir is Scientific Supervisor of the Economic Research Institute (ERI), FEB RAS. Natal’ya Gennad’evna Dzhurka, Cand. Sci. (Econ.), is Senior Researcher at the same institute.
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Minakir, P.A., Dzhurka, N.G. The Methodological Foundations of Spatial Studies in Economics. Her. Russ. Acad. Sci. 88, 281–288 (2018). https://doi.org/10.1134/S1019331618040044
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DOI: https://doi.org/10.1134/S1019331618040044