FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 7, PAGES 3-14

Local connectedness of suns in normed linear spaces

A. R. Alimov

Abstract

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The paper is concerned with solarity of intersections of suns with bars (in particular, with closed balls and extreme hyperstrips) in normed linear spaces. A sun in a finite-dimensional (BM)-space (in particular, in $$l¹(n)) is shown to be monotone path connected. A nonempty intersection of an $m$-connected set (in particular, a sun in a two-dimensional space or in a finite-dimensional (BM)-space) with a bar is shown to be a monotone path-connected sun. Similar results are obtained for boundedly compact subsets of infinite-dimensional spaces. A nonempty intersection of a monotone path-connected subset of a normed space with a bar is shown to be a monotone path-connected $$a-sun.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k117/k11701h.htm
Last modified: May 24, 2013