Internally Disclosed Sets of a Real Space (Contemporary Mathematics, 2024)
There is no single set in a real space, for which an exact mathematical definition would not exist by the mathematical symmetry laws. We discuss a theory in which a real number axis is defined at the new level, namely, at the level of real space allowing one to formulate and prove the theorem on the basis of its internal disclosure. This new theory of a set makes it possible to introduce a notion of the full compactness of sets of a real space, confirming their availability in the defined symmetry of elements of a definitely symmetrical line.
Keywords: real space; algebraical logic; geometrical logic; mathematically united logic; regular sets; casual sets; real number axis; full compactness of a set; logic of the commutativity law; full finiteness of a set