I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2011/2012, VOLUME 17, NUMBER 1, PAGES 23-32
Monotone path-connectedness of -weakly
convex sets in the space
A. R. Alimov
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A subset of a normed linear
said to be -weakly convex
fixed) if the intersection is nonempty for all
Here is the
intersection of all the balls of radius that contain , .
The paper is concerned with connectedness of -weakly convex sets in
It will be shown that any -weakly convex
locally -connected (locally Menger-connected) and each
connected component of a boundedly compact -weakly convex
monotone path-connected and is a sun in .
Also, we show that a boundedly compact subset of is -weakly convex for some
only if is
a disjoint union of monotonically path-connected suns in
Hausdorff distance between each pair of the components
at least .
Last modified: January 31, 2012