The nature of the topological intuition
Liberal Arts in Russia. 2016. Vol. 5. No. 1. Pp. 14-21.Get the full text (Russian)Email: firstname.lastname@example.org
The article is devoted to the nature of the topological intuition and disclosure of the specifics of topological heuristics in the framework of philosophical theory of knowledge. As we know, intuition is a one of the support categories of the theory of knowledge, the driving force of scientific research. Great importance is mathematical intuition for the solution of non-standard problems, for which there is no algorithm for such a solution. In such cases, the mathematician addresses the so-called heuristics, built on the basis of guesswork, obtained by intuition. The author substantiates the conclusion that topological intuition significantly specific compared to a traditional mathematical intuitions of Euclidean geometry. Today topology is a rapidly developing field of modern mathematics, integrates nicely with other sections of mathematical science. In its most general form of the topology can be defined as the branch of mathematics that studies the properties of spatial figures, does not change under deformations. The topological intuition is an instrument for development of topology on the basis of typological heuristics, which is the result of applying topological intuition to the objects topology. The author demonstrates in detail providing with the examples the specificity of topological heuristics and establishes its interconnection with Euclidean geometry. The author draws the conclusion about the fundamentality of topological intuition, and that it, perhaps, is primary in relation to traditionally understood mathematical intuition.
- • topological heuristics
- • topological studies in mathematics
- • mathematical heuristics
- • topological heuristics
- • heuristic conversion topology
- • elementary geometry
- • initial intuition
- • univalent foundations of mathematics
- • implicit elements of knowledge
- • a priori in mathematics
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