Genesis of topological views through network approach

The article is devoted to theoretical reflection of the source of the topological area of social network research. The article traces the paths of social topology development as a special methodology lens used within the network approach and originated from mathematical topology. The divisions of non mathematical topology into two branches - topology of space described in works by Kurt Lewin and Pierre Bourdieu, and topology of form defined by Rene Thom - have been substantiated in this work. According to the above-mentioned dvision, the mechanisms of topological tool application are studied in the works of the scientists who represent such main areas of the network approach as: analysis of social networks, relational sociology, and actor-network theory. It has been found that the followers of social network analysis and relational sociology are inclined to use the topological tools for determining the position of the object in a symbolic social space and emphasize its interrelations with other objects (topology of space). Moreover, the former makes use of topology as a clear method for constructing the so-called spatial maps, graphs, and plots, the latter - as a descriptive method which is far from illustrativeness. The works of John Lo, a supporter of actor-network theory, are devoted to topological instruments used for investigating the objects of network nature which possess inner dimensionality (the topology of form). Through understanding that a social object exists in the majority of spaces (regions, networks and flows are to be mentioned), a symbolic social form is constituted. On the basis of the conclusions drawn analytically, it is claimed that social topology takes the main research traits from mathematical topology and concentrates its interest both on studying the location of objects in symbolic space and spatial forms research. The decisive role in choosing the means of topology-methodology lens application belongs to a symbolic agreement on the main ontological and theoretical issues between the researchers of different areas. It is concluded that common topological views can be extended through the understanding of topology as a synthetic instrument incorporating best practices of topology both of space and form on the main ontological and theoretical issues.

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