Measuring Soft Structures: Their Metric and Topological Dimensions

Purpose: Measurability and metrics are the domain of mathematics.And it is this mathematics that created the branch (discipline) called Measure Theory.Mathematics also created more general fields than the measurable one (linear Euclidean space).These are topology, algebraic topology and category theory, which science tries to apply even to the description, to the grasp of the structures of the humanities.And this is the main dimension of the content of the article.Design/Methodology/Approach: Praxeology is an extremely important field of knowledge, because it is somehow connected with both theory and practice.On the one hand, it examines the invariants (patterns, structures) of all human actions, and on the other hand, it has a utilitarian goal, the goal of using the invariants learned in practice, and perhaps even primarily in the humanities (because mathematics has its own research tools related to it.These are measurable, topological and from the area of category theory, transformation theory).All of them together constitute the methodological dimension of the content of the article.Practical Implications: Generally speaking, in practice we deal with three categories of processes.These are physical, biological, social and mental processes of a human being.The latter are difficult to formalize, i.e. to express their structures in metric terms, and especially mental processes of a human being.And in the text we show what methods of mathematics can be used to capture the processes of the human locus.The praxeological dimension of science combines precision (patterns) with soft structures, because these are also human actions, these everyday ones (you also have to be able to express them scientifically).In addition, there is also a created dimension of science called Pragmatics.All actions are expressed in processes, or rather through them, through their categories.And this dimension of methodology is reflected in the article in the practical dimension indicating the application of the methods presented there.