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Nearest points to closed sets and directional derivatives of distance functions
Simon Fitzpatrick
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Source: Crossref
Published: Apr 1, 1989
DOI: 10.1017/s0004972700002707
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We investigate the circumstances under which the distance function to a closed set in a Banach space having a one-sided directional derivative equal to 1 or −1 implies the existence of nearest points. In reflexive spaces we show that at a dense set of points outside a closed set the distance function has a directional derivative equal to 1.
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