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 $$*l*^{1}(n))
is shown to be monotone path connected.
A nonempty intersection of an
$m$-connected set
(in particular, a sun in a two-dimensional space or in
a finite-dimensional (*BM*)-space) with a bar is shown
to be a monotone path-connected sun.
Similar results are obtained for boundedly compact subsets of
infinite-dimensional spaces.
A nonempty intersection of a monotone path-connected subset
of a normed space with a bar is shown to be a monotone
path-connected $$a-sun.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k117/k11701h.htm

Last modified: May 24, 2013