Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convexity of Balls in Gromov--Hausdorff Space   In this paper we study the space $\mathcal{M}$ of all nonempty compact metric
spaces considered up to isometry, equipped with the Gromov--Hausdorff distance.
We show that each ball in $\mathcal{M}$ with center at the one-point space is
convex in the weak sense, i.e., every two points of such a ball can be joined
by a shortest curve that belongs to this ball, however, such a ball is not
convex in the strong sense: it is not true that every shortest curve joining
the points of the ball belongs to this ball. We also show that a ball of
sufficiently small radius with center at a space of general position is convex
in the weak sense.

1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol