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- W1616655656 abstract "This note is purely expository. We show how in the course of the Kolmogorov-Arnold solution of Hilbert's 13-th problem on superpositions there appeared the notion of a basic embedding. A subset K of R^2 is {it basic} if for each continuous function f:K->R there exist continuous functions g,h:R->R such that f(x,y) = g(x) + h(y) for each point (x,y) in K. We present descriptions of basic subsets of the plane and graphs basically embeddable into the plane (solutions of Arnold's and Sternfeld's problems). We present some results and open problems on the smooth version of the property of being basic. This note is accessible to undergraduates and could be an interesting easy reading for mature mathematicians." @default.
- W1616655656 created "2016-06-24" @default.
- W1616655656 creator A5080902504 @default.
- W1616655656 date "2010-01-22" @default.
- W1616655656 modified "2023-09-27" @default.
- W1616655656 title "Basic embeddings and Hilbert's 13th problem on superpositions (in Russian)" @default.
- W1616655656 hasPublicationYear "2010" @default.
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