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Siberian Mathematical Journal

, Volume 58, Issue 1, pp 11–15 | Cite as

A monotone path-connected set with outer radially lower continuous metric projection is a strict sun

  • A. R. Alimov
Article
  • 25 Downloads

Abstract

A monotone path-connected set is known to be a sun in a finite-dimensional Banach space. We show that a B-sun (a set whose intersection with each closed ball is a sun or empty) is a sun. We prove that in this event a B-sun with ORL-continuous (outer radially lower continuous) metric projection is a strict sun. This partially converses one well-known result of Brosowski and Deutsch. We also show that a B-solar LG-set (a global minimizer) is a B-connected strict sun.

Keywords

sun strict sun monotone path-connected set radial continuity of the metric projection 

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References

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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia

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