Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local convexity in CAT(\kappa)-spaces   Heinrich Tietze has shown that for a closed connected subset of euclidean
space being convex is a local property. We generalize this to CAT(0)-spaces and
locally compact CAT(\kappa) spaces. As an application we give a construction of
certain convex sets in euclidean buildings.

14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th