Sets of discontinuities of linearly continuous functions (Q2510965)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sets of discontinuities of linearly continuous functions |
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Sets of discontinuities of linearly continuous functions (English)
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5 August 2014
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The set \(D(f)\) of the discontinuities of a linearly continuous function \(f:\mathbb{R}^n \to \mathbb{R}\) is characterized. This set is a countable union of sets that are isometric to the graph of a Lipschitz function defined on an \((n-1)\)-dimensional compact set. Finally, two open problems are posed.
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separate continuity
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linear continuity
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discontinuity sets
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