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arXiv · 1401.3273

A qualitative description of graphs of discontinuous polynomial functions

J. M. Almira·Kh. F. Abu-Helaiel
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Abstract

We prove that, if f:R^n\to R satisfies Fr\'echet's functional equation and f(x_1,...,x_n) is not an ordinary algebraic polynomial in the variables x_1,...,x_n, then f is unbounded on all non-empty open set U of R^n. Furthermore, the closure of its graph contains an unbounded open set.

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J. M. Almira, Kh. F. Abu-Helaiel. 2014-01-14. A qualitative description of graphs of discontinuous polynomial functions. https://arxiv.org/abs/1401.3273

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