Existence of continuous right inverses to linear mappings in finite-dimensional geometry
A linear mapping of a compact convex subset of a finite-dimensional vector space always possesses a right inverse, but may lack a continuous right inverse, even if the set is smoothly bounded. Examples showing this are given, as well as conditions guaranteeing the existence of a continuous right inv...
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Veröffentlicht in: | Mathematische Semesterberichte 2021, Vol.68 (1), p.55-68 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | A linear mapping of a compact convex subset of a finite-dimensional vector space always possesses a right inverse, but may lack a continuous right inverse, even if the set is smoothly bounded. Examples showing this are given, as well as conditions guaranteeing the existence of a continuous right inverse. |
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ISSN: | 0720-728X 1432-1815 1432-1815 |
DOI: | 10.1007/s00591-020-00286-0 |