A monotone path-connected set with outer radially lower continuous metric projection is a strict sun
- Authors: Alimov A.R.1
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Affiliations:
- Moscow State University
- Issue: Vol 58, No 1 (2017)
- Pages: 11-15
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/170905
- DOI: https://doi.org/10.1134/S0037446617010025
- ID: 170905
Cite item
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.
About the authors
A. R. Alimov
Moscow State University
Author for correspondence.
Email: alexey.alimov-msu@yandex.ru
Russian Federation, Moscow