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
Hauptverfasser: Kiselman, Christer Oscar, Melin, Erik
Format: Artikel
Sprache:eng
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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.
ISSN:0720-728X
1432-1815
1432-1815
DOI:10.1007/s00591-020-00286-0