Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniformly convex metric spaces   In this paper the theory of uniformly convex metric spaces is developed.
These spaces exhibit a generalized convexity of the metric from a fixed point.
Using a (nearly) uniform convexity property a simple proof of reflexivity is
presented and a weak topology of such spaces is analyzed. This topology called
co-convex topology agrees with the usualy weak topology in Banach spaces. An
example of a $CAT(0)$-spaces with weak topology which is not Hausdorff is
given. This answers questions raised by Monod 2006, Kirk and Panyanak 2008 and
Esp\'inola and Fern\'andez-Le\'on 2009.
  In the end existence and uniqueness of generalized barycenters is shown and a
Banach-Saks property is proved.

15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
18
The categories of this paper are: econ
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin