A dichotomy property for the graphs of monomials
We prove that the graph of a discontinuous $n$-monomial function $f:\mathbb{R}\to\mathbb{R}$ is either connected or totally disconnected. Furthermore, the discontinuous monomial functions with connected graph are characterized as those satisfying a certain big graph property. Finally, the connectedn...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
30.10.2014
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Subjects | |
Online Access | Get full text |
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Summary: | We prove that the graph of a discontinuous $n$-monomial function
$f:\mathbb{R}\to\mathbb{R}$ is either connected or totally disconnected.
Furthermore, the discontinuous monomial functions with connected graph are
characterized as those satisfying a certain big graph property. Finally, the
connectedness properties of the graphs of additive functions
$f:\mathbb{R}^d\to\mathbb{R}$ are studied. |
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DOI: | 10.48550/arxiv.1410.8468 |