Mathematics – Functional Analysis
Scientific paper
2010-03-08
Mathematics
Functional Analysis
14 pages, 6 figures
Scientific paper
This note is purely expository. In the course of the Kolmogorov-Arnold solution of Hilbert's 13th problem on superpositions there appeared the notion of basic embedding. A subset K of R^2 is 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 (with a proof) and description of 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. The two sections can be read independently on each other.
No associations
LandOfFree
Basic embeddings and Hilbert's 13th problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Basic embeddings and Hilbert's 13th problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Basic embeddings and Hilbert's 13th problem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-676941