A monotone path-connected set with outer radially lower continuous metric projection is a strict sun
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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.
Keywordssun strict sun monotone path-connected set radial continuity of the metric projection
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- 7.Flerov A. A., Selected Geometric Properties of Sets with Finite-Valued Metric Projection [Russian], Diss. Kand. Fiz.-Mat. Nauk, Moscow Univ., Moscow (2016).Google Scholar