A qualitative description of graphs of discontinuous polynomial functions
Abstract
We prove that, if f:Rn R satisfies Fr\'echet's functional equation and f(x1,...,xn) is not an ordinary algebraic polynomial in the variables x1,...,xn, then f is unbounded on all non-empty open set U of Rn. Furthermore, the closure of its graph contains an unbounded open set.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.