Geodesic
Principles of rational analysis - continuity of functions
Nečetkie sistemy i mâgkie vyčisleniâ, Tome 14 (2019) no. 2, pp. 126-141.

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A mathematical apparatus is proposed for constructing analysis on a set of rational numbers. Soft boundaries of sets, soft limit, soft continuity of rational functions are introduced. Extreme proximity maps for the soft continuity of the function are found. For soft continuity, analogues of the properties of classical continuous functions are proved. The concept of approximation of a real function using a rational function is introduced. It is proved that both the approximated and the approximating functions must have soft continuity properties.
Keywords: rational analysis, soft continuity of rational function, soft limit of rational function, soft approximation. 
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     title = {Principles of rational analysis - continuity of functions},
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D. A. Molodtsov. Principles of rational analysis - continuity of functions. Nečetkie sistemy i mâgkie vyčisleniâ, Tome 14 (2019) no. 2, pp. 126-141. http://geodesic.mathdoc.fr/item/FSSC_2019_14_2_a3/

[1] Molodtsov D. A., “Soft Set Theory - First Results”, Computers and Mathematics with Applications, 37 (1999), 19–31

[2] Kuratovskij K., Topology, v. 1, Mir Publ., Moscow, 1966 (in Russian)

[3] Molodtsov D. A., Soft set theory, URSS Publ., Moscow, 2004 (in Russian)